Find the exact length of the curve calculator

Graph the curve and find its length. x = cos t + ln (tan1/2t), y = sin t, π/4≤t≤3π/4. calculus. If a and b are fixed numbers, find parametric equations for the set of all points P determined as shown in the figure, using the angle \theta θ as the parameter. The line segment A B AB is tangent to the larger circle.

Let be a smooth curve in a manifold from to with and .Then where is the tangent space of at .The length of with respect to the Riemannian structure is given byMay 28, 2018 · Arc length is given by: L = ∫ 1 0 √(sint + tcost)2 + (cost − tsint)2dt. Expand and simplify: L = ∫ 1 0 √1 + t2dt. Apply the substitution t = tanθ: L = ∫ tan−1(1) 0 sec3θdθ. This is a known integral. If you do not have it memorized look it up in a table of integrals or apply integration by parts: L = 1 2[secθtanθ + ln|secθ ... To estimate the area under the graph of f f with this approximation, we just need to add up the areas of all the rectangles. Using summation notation, the sum of the areas of all n n rectangles for i = 0, 1, …, n − 1 i = 0, 1, …, n − 1 is. Area of rectangles =∑ i=0n−1 f(xi)Δx. (1) (1) Area of rectangles = ∑ i = 0 n − 1 f ( x i ...Answer link. In Cartesian coordinates for y = f (x) defined on interval [a,b] the length of the curve is =>L = int_a^b sqrt (1+ ( (dy)/ (dx))^2) dx In general, we could just write: => L = int_a^b ds Let's use Cartesian coordinates for this explanation. If we consider an arbitrary curve defined as y = f (x) and are interested in the interval x ...We now need to look at a couple of Calculus II topics in terms of parametric equations. In this section we will look at the arc length of the parametric curve given by, x = f (t) y =g(t) α ≤ t ≤ β x = f ( t) y = g ( t) α ≤ t ≤ β. We will also be assuming that the curve is traced out exactly once as t t increases from α α to β β.

Arc length Cartesian Coordinates. Arc Length of 2D Parametric Curve. Arc Length of 3D Parametric Curve. Math24.pro. Free Arc Length of Polar Curve calculator - Find the arc length of functions between intervals step-by-step.You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: (1) Compute the length of the curve f (x) = x 3/2 , for 0 x 4. (2) Compute the length of the curve f (x) =x3 / 3 + 1 / 4x, for 1 x 2. (3) Compute the length of the curve f (x) =. (1) Compute the length of the curve f (x) = x 3/2 , for 0 x 4 ...Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Find Arc Length of a Curve...How to calculate Length of Curve using this online calculator? To use this online calculator for Length of Curve, enter Curve Radius (RCurve) & Deflection Angle (Δ) and hit the calculate button. Here is how the Length of Curve calculation can be explained with given input values -> 226.8928 = 200*1.1344640137961.Calculus. Calculus questions and answers. Find the arc length of the curvef (x)=ln (cos x)over the interval [0,pi/4]Here is what I have so far, but I cannot come up with theright answer.L= integral 0 to pi/4 √ (1+tan^2x) dxL= integral 0 to pi/4 √ (sec^2x) dxL=integral 0 to pi/4 secxL= [sec * pi/4]A: First find the intersection point of the curve then calculate slope of tangents of both the curve at… Q: Use the guidelines of curve sketching to sketch the curve y = 1-x2 %3D A: Given: y=x1-x2Calculus. Calculus questions and answers. Find the exact length of the curve. y = 5 + 6x3/2, 0 ≤ x ≤ 1.If the angle is equal to 360 degrees or 2 π, then the arc length will be equal to circumference. Furthermore, the proportion between angle and arc length remains constant, so the arc length equation will be: • L / θ = C / 2 π. • In the formula for arc length the circumference C = 2 π r. • L / θ = 2 π r / 2 π.

31 de dez. de 2022 ... Arc Length - Formula, How to Find Length of an Arc, Examples. Arc ... Once again, using the pie tool and an arc calculator I get a size correct to ...The exact length is thus ln| sec(3/2) + tan(3/2)| ln | sec ( 3 / 2) + tan ( 3 / 2) |. Using a calculator to find the length to 3 3 decimal places gives: s = 3.341 s = 3.341 . We saw that the length of the curve on the interval [0, 3/2] [ 0, 3 / 2] is given by which can be interpreted conceptually as. It is easy to see that the curve is a circle of radius 1. It's length is obviously #2pi# A more analytic solution would go as follows. #ds^2 = dr^2+r^2d theta^2# So, for #r = 2 cos theta#, we have. #dr = -2 sin theta d theta# and hence. #ds^2 = (-2 sin theta d theta)^2+(2 cos theta)^2 d theta^2 = 4d theta^2 implies# #ds = 2 d theta# Thus, the ...To find the Arc Length, we must first find the integral of the derivative sum given below: L a r c = ∫ a b ( d x d t) 2 + ( d y d t) 2 d t. Placing our values inside this equation gives us the arc length L a r c: L a r c = ∫ 0 9 ( d ( − …Final answer. Find the exact length of the curve. x = 2+ 6t2, y = 6+ 4t3, 0 ≤ t ≤ 5 Enhanced Feedback Please try again, keeping in mind that the are length formula for parametric curves is L = ∫ αβ (dtdx)2 + (dtdy)2dt.

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A vector length is another way of saying a vector magnitude. It's a measure of distant from the origin 0,0,0 to the coordinate points of the vector. Enter the 3 coordinate points of a vector into the vector length calculator. The calculator will return the total vector magnitude (length).Limits at infinity are used to describe the behavior of a function as the input to the function becomes very large. Specifically, the limit at infinity of a function f (x) is the value that the function approaches as x becomes very large (positive infinity). what is a one-sided limit?Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Find the exact length of the curve. x = 2 3t3, y = t2 − 2, 0 ≤ t ≤ 2. BUY. Trigonometry (MindTap Course List) 8th Edition. ISBN: 9781305652224. Author: ... Let's say the length of the curve is L. 0 ≤ t ≤ 1 Hence, the desired length will be calculated as: Q: a)Find the exact length L of the curve 3y = (4x – 3), 1 0. Answer: b ...

To determine the length and width of a rectangle given area and perimeter: State the equations for both area (A) and perimeter (P). A = length (L) × width (W) P = 2L + 2W. From the first equation, we can also express W as: W = P/ (2-L) Putting this into the second equation will look like this: A = L × P/ (2-L), or:The Length of Curve Calculator finds the arc length of the curve of the given interval. The curve length can be of various types like Explicit, Parameterized, Polar, or Vector curve. What is the Length of the Curve?Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. See Answer. Question: Find the exact length of the polar curve r=cos4 (θ/4). Length =?Find the exact length of the curve? #y=x^3/3+1/(4x)#, #1\lex\le2# Calculus Applications of Definite Integrals Determining the Length of a Curve. 1 Answer Anjali G Oct 14, 2017 #"Length" = 59/24 approx 2.4583# Explanation: The ... How do you find the length of a curve using integration?Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. x=t^2-t, y = t^4, 1 ≤ t ≤ 4. x= t2 −t,y = t4,1 ≤ t≤ 4. biology. Archaea are more closely related to _ than _. calculus.10. + 0/1 points Previous Answers SCalcET8 10.2.041. My Not Find the exact length of the curve. x = 4 + 3t2, y = 5 + 2t3, Osts 2 Enhanced Feedback Please try again, keeping in mind that the arc length formula for parametric curves is L arc length formula for parametric curves is L = L." ( * + ( ) dt.where R represents the radius of the helix, h represents the height (distance between two consecutive turns), and the helix completes N turns. Let’s derive a formula for the arc length of this helix using Equation 13.3.4. First of all, ⇀ r′ (t) = − 2πNR h sin(2πNt h)ˆi + 2πNR h cos(2πNt h)ˆj + ˆk.Find the exact arc length of the curve on the given interval. Parametric Equations Interval x = t 2 + 1, y = 2 t 3 + 7 0 ≤ t ≤ 2. Get more help from Chegg . Solve it with our Calculus problem solver and calculator. Not the exact question you're looking for? Post any question and get expert help quickly. Start learning . Chegg Products ...The tangent line calculator finds the equation of the tangent line to a given curve at a given point. Step 2: Click the blue arrow to submit. Choose "Find the Tangent Line at the Point" from the topic selector and click to see the result in our Calculus Calculator ! Examples . Find the Tangent Line at (1,0) Popular Problems

Find the exact length of the curve 4V'î 3/2 _ SOLUTION for 1/2 = dx which is continuous on [0, l]. Therefore, dy dx —(1 + 8x)3/2 13 dx Now try Exercise 11. In Exercises I I—18, find the exact length of the curve analytically by antidifferentiation. You will need to …

The arc length, L, along the curve y = f(x) from x = a to x = b is given by. L = ∫b a√1 + f ′ (x)2dx. A single definite integral may be used to represent the area between two curves. To find the area between two curves, we think about slicing the region into thin rectangles. The shape of the region ….Parametric Arc Length. Inputs the parametric equations of a curve, and outputs the length of the curve. Note: Set z (t) = 0 if the curve is only 2 dimensional. Get the free "Parametric Arc Length" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. Arc length is given by: L = ∫ 1 0 √(sint + tcost)2 + (cost − tsint)2dt. Expand and simplify: L = ∫ 1 0 √1 + t2dt. Apply the substitution t = tanθ: L = ∫ tan−1(1) 0 sec3θdθ. This is a known integral. If you do not have it memorized look it up in a table of integrals or apply integration by parts: L = 1 2[secθtanθ + ln|secθ ...To find the length of a line segment with endpoints: Use the distance formula: d = √ [ (x₂ - x₁)² + (y₂ - y₁)²] Replace the values for the coordinates of the endpoints, (x₁, y₁) and (x₂, y₂). Perform the calculations to get the value of the length of the line segment.Find the length of the curve of the vector values function x=17t^3+15t^2-13t+10, y=19t^3+2t^2-9t+11, and z=6t^3+7t^2-7t+10, the upper limit is “2” and the lower limit is “5”. Given: Lower limit= 5, upper limit = 2. Sol: The length of the curve is given by: L = ∫ a b ( x ′ ( t)) 2 + ( y ′ ( t)) 2 + ( z ′ ( t)) 2 d t. The polar arc length of a curve is given by: L = ∫ β α √r2 +( dr dθ)2 dθ. We have: r = a(1 − cosθ) = a −acosθ. Thus: dr dθ = asinθ. So, the arc length is: L = ∫ 2π 0 √(a −acosθ)2 +(asinθ)2 dθ.Find the arc length of a curve. Problem integrating. 2. Question about length of curve? 1. Evaluating line integral on the curve. 0. Finding Second Derivative using implicit differentiation. 1. Finding Arc Length of a curve. 0. moving particle submitted to a law of motion. 1.Problem 49 Easy Difficulty. Find the exact length of the curve. Use a graph to determine the parameter interval. $$ r=\cos ^{4}(\theta / 4) $$

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The arc-length function for a vector-valued function is calculated using the integral formula s(t) = ∫b a‖ ⇀ r ′ (t)‖dt. This formula is valid in both two and three dimensions. The curvature of a curve at a point in either two or three dimensions is defined to be the curvature of the inscribed circle at that point.Graph the curve. x = 3et cos t, y = 3et sin t, 0 t pi Find the exact length of the curve. Get more help from Chegg . Solve it with our Calculus problem solver and calculator. Not the exact question you're looking for? Post any question and get expert help quickly. Start learning . Chegg Products & Services.Enter the given values.Our leg a is 10 ft long, and the α angle between the ladder and the ground equals 75.5°.. Ladder length, our right triangle hypotenuse, appears! It's equal to 10.33 ft. The angle β = 14.5° and leg b = 2.586 ft are displayed as well. The second leg is also an important parameter, as it tells you how far you should place the ladder from the wall (or rather from a roof ...To find the arc length of a parametric curve, we have to assume two facts: (1) as t goes from a to b, we trace the curve exactly once; (2) as t increases, x also increases. (This way, we prevent our parametrization from "reversing" directions at any point.) Given these assumptions, the arc length is equal to. L=∫ba√ (dxdt)2+ (dydt)2dt.What is a basic trigonometric equation? A basic trigonometric equation has the form sin (x)=a, cos (x)=a, tan (x)=a, cot (x)=a. How to convert radians to degrees? The formula to convert radians to degrees: degrees = radians * 180 / π. What is cotangent equal to?This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: 3. (15 points) Find the exact length of the polar curve given by r=3sin (θ) where we have that 0≤θ≤π/3. Using your prior knowledge of high school geometry, how can you be sure that your answer is correct ...Learning Objectives. 7.2.1 Determine derivatives and equations of tangents for parametric curves.; 7.2.2 Find the area under a parametric curve.; 7.2.3 Use the equation for arc length of a parametric curve. To find the distance between two points we will use the distance formula: √ [ (x₂ - x₁)² + (y₂ - y₁)²]: Get the coordinates of both points in space. Subtract the x-coordinates of one point from the other, same for the y components. Square both results separately. Sum the values you got in the previous step.We start by asking how to calculate the slope of a line tangent to a parametric curve at a point. Consider the plane curve defined by the parametric equations. x (t)=2t+3,y (t)=3t−4,−2≤t≤3. The graph of this curve appears in [link]. It is a line segment starting at (−1,−10) and ending at (9,5). ….

Circular Curve Calculator. Enter. Input, Radius or Degree, AND, Delta or Length. Radius, Delta, º ' ". Degree, º ' ", Length. August 2000.You will see that the curve is covered exactly once in the interval [0, 2π) [ 0, 2 π). You can also calculate some points for various values of theta and see that there is no repetition on that interval. Therefore, letting r(θ) = 2(1 + cos θ) r ( θ) = 2 ( 1 + cos θ) the arc length is given by.Arc Length Formula (s) L = ∫ds. where, ds = √1 + (dy dx)2dx if y = f(x), a ≤ x ≤ b ds = √1 + (dx dy)2dy if x = h(y), c ≤ y ≤ d. Note that no limits were put on the integral as the limits will depend upon the ds that we’re using. Using the first ds will require x limits of integration and using the second ds will require y limits ...Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.) r ( t ) = sin ( t ) , cos ( t ) , tan ( t ) , 0 ≤ t ≤ 4 π Get more help from Cheggrobshowsides. The arclength in the x-y plane is ALWAYS ∫ √ ( dx² + dy²). Thus, if you are given x (t) and y (t) (we say "parametric" equations for x and y), then we can write this as: Basically, we have "divided" everything inside the radical by dt², and so we then multiply on the outside of the radical simply by dt. Find step-by-step Calculus solutions and your answer to the following textbook question: Find the exact length of the curve. y = 1/4x2 - 1/2 In x, 1≤ x ≤ 2.Arc length Cartesian Coordinates. Arc Length of 2D Parametric Curve. Arc Length of 3D Parametric Curve. Math24.pro. Free Arc Length of Polar Curve calculator - Find the arc length of functions between intervals step-by-step.Find step-by-step Calculus solutions and your answer to the following textbook question: Find the exact arc length of the curve over the stated interval. x=cos3t, y=sin3t, $$ ( 0 \leq t \leq \pi ) $$.Find the length of the curve defined by the parametric equations. x= 4/5 * t. y=4ln((t/5)^2-1) from t = 9 to t = 10. ... Solve it with our Calculus problem solver and calculator. Not the exact question you're looking for? Post any question and get expert help quickly. Find the exact length of the curve calculator, Calculate the arc length according to the formula above: L = r × θ = 15 × π/4 = 11.78 cm. Calculate the area of a sector: A = r² × θ / 2 = 15² × π/4 / 2 = 88.36 cm². You can also use the arc length calculator to find the central angle or the circle's radius. Simply input any two values into the appropriate boxes and watch it ..., Is it true that we can measure the exact length of that curve just using the differential/calculus function or some sort? calculus; Share. Cite. Follow edited Dec 20, 2015 at 23:18. user9464 asked Dec 20, 2015 at 23:11. lina lawrence lina lawrence. 23 3 3 bronze badges $\endgroup$ 2 ..., Find the length of the curve r(t)= $<t^2,2t,lnt> $ from t=1 to t=e i know that Length= $\int$ length of r'(t) dt Therefore, L= $\int _1^e\sqrt{4t^2+4+\frac{1}{t^2}}dt\$$ but i'm having trouble with solving this integral? i would think of u sub but having trouble what to set u equal to if that's even the approach i should be taking?, See Answer. Question: Find the exact length of the curve. y^2 = 64 (x + 4)^3, 0 lessthanorequalto x lessthanorequalto 2, y > 0 For a curve given by y = f (x), arc length is given by: We have y^2 = 64 (x + 4)^3, y > 0 which can be re-written as follows. Now, dy/dx = 12 (x + 4)^ (1/2) The arc length can be found by the integral: L = integral^2_0 ..., Question: Find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 3 Find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 3 Expert Answer, Question: Find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 3 Find the exact length of the curve. x = y4 8 + 1 4y2 , 1 ≤ y ≤ 3 Expert Answer, 1.)Find the exact length of the curve : y2 = 4 (x + 1)3, 0 ? x ? 3, y > 0 2.)Find the exact length of the curve: 3.) A triangular plate with height 4 ft and a base of 6 ft is submerged vertically in water so that the top is 2 ft below the surface. Express the hydrostatic force against one side of the plate as an integral and evaluate it., This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: 3. (15 points) Find the exact length of the polar curve given by r=3sin (θ) where we have that 0≤θ≤π/3. Using your prior knowledge of high school geometry, how can you be sure that your answer is correct ..., Finding the length of the parametric curve 𝘹=cos(𝑡), 𝘺=sin(𝑡) from 𝑡=0 to 𝑡=π/2, using the formula for arc length of a parametric curve., If θ goes from θ1 to θ2, then the arc length is √2(eθ2 − eθ1). Let us look at some details. L = ∫ θ2 θ1 √r2 +( dr dθ)2 dθ. since r = eθ and dr dθ = eθ, = ∫ θ2 θ1 √(eθ)2 + (eθ)2 dθ. by pulling eθ out of the square-root, = ∫ θ2 θ1 eθ√2dθ = √2∫ θ2 θ1 eθdθ. by evaluating the integral,, Free Arc Length calculator - Find the arc length of functions between intervals step-by-step, Learning Objectives. 1.2.1 Determine derivatives and equations of tangents for parametric curves.; 1.2.2 Find the area under a parametric curve.; 1.2.3 Use the equation for arc length of a parametric curve.; 1.2.4 Apply the formula for surface area to a volume generated by a parametric curve., Here we derive a formula for the arc length of a curve defined in polar coordinates. In rectangular coordinates, the arc length of a parameterized curve (x(t), y(t)) for a ≤ t ≤ b is given by. L = ∫b a√(dx dt)2 + (dy dt)2dt. In polar coordinates we define the curve by the equation r = f(θ), where α ≤ θ ≤ β., 1. Edit: Update with the full question for context. Find the exact length of the curve y = ln(1 −x2), 0 ≤ x ≤ 1 2 y = ln ( 1 − x 2), 0 ≤ x ≤ 1 2. The integral below is what I got after finding the derivative −2 1−x2 − 2 1 − x 2 via the chain rule. Can someone give me a hint on how to evaluate this integral with a range of 0 ..., 1. Determine the length of the following polar curve. You may assume that the curve traces out exactly once for the given range of θ θ . r =−4sinθ, 0 ≤ θ ≤ π r = − 4 sin. ⁡. θ, 0 ≤ θ ≤ π Solution. For problems 2 and 3 set up, but do not evaluate, an integral that gives the length of the given polar curve. For these ..., Find the exact length of the curve. 36y2 = (x2 − 4)3, 5 ≤ x ≤ 6, y ≥ 0. Problem 1RE: For the following exercises, write the quadratic function in standard form. Then, give the vertex... Problem 2RE: For the following exercises, write the quadratic function in standard form., The concepts we used to find the arc length of a curve can be extended to find the surface area of a surface of revolution. ... It may be necessary to use a computer or calculator to approximate the values of the integrals. Key Equations. Arc Length of a Function of x; Arc Length \( =∫^b_a\sqrt{1+[f′(x)]^2}dx\), When the curve is below the axis the value of the integral is negative! So we get a "net" value. Total Area. If we want a total area (say we wanted to paint it) we can use the absolute value function abs(). Or we can manually find where the curve crosses the axis and then work out separate integrals and reverse the negatives before adding., Lets use the above formula to calculate the arc length of circle. arc length = (central angle x π/180 ) x radius. arc length = (25 x π/180 ) x 3. arc length = (25 x π/180 ) x 3. arc length = (0.43633231299 ) x 3. arc length = 1.308996939 m. Example 2 : Find arc length of a wooden wheel with diameter measuring 3 ft and central angle of 45 ..., A: First find the intersection point of the curve then calculate slope of tangents of both the curve at… Q: Sketch the graph of the curve r = 2+4Cose A: Given equation: r=2+4 cos θAmplitude: 4This equation will have the same time periodas sinθ which is…, Enter the Function you want to domain into the editor. The domain calculator allows you to take a simple or complex function and find the domain in both interval and set notation instantly. Step 2: Click the blue arrow to submit and see the result! The domain calculator allows to find the domain of functions and expressions and receive results ..., Summary of the Riemann Sum Method for Arc Length: Here are the steps in the modeling process of using Riemann Sums to find the arc length of a curve in the ..., Find the length of the curve correct to four decimal places. (Use your calculator to approximate the integral.) r ( t ) = sin ( t ) , cos ( t ) , tan ( t ) , 0 ≤ t ≤ 4 π Get more help from Chegg, Now we must use |sin(3t)| to calculate length. If we didn't use absolute values, then we would just be calculating length of straight line from first point to last point on curve. now sin(3t) >= 0 on intervals [0,π/3] and [2π/3,π], Find step-by-step Calculus solutions and your answer to the following textbook question: Find the exact length of the curve. $$ x=\frac{2}{3} t^{3}, \quad y=t^{2}-2, \quad 0 \leqslant t \leqslant 3 $$. ... Then use your calculator to find the length correct to four decimal places., Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. x=t^2-t, y = t^4, 1 ≤ t ≤ 4. x= t2 −t,y = t4,1 ≤ t≤ 4. biology. Archaea are more closely related to _ than _. calculus., Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more., Transcribed image text: Find the exact length of the polar curve. r = 3cos(θ), 0 ≤ θ ≤ π Find the exact length of the curve. Use a graph to determine the parameter interval. r = cos4(4θ) Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r = 8cos(θ), θ = 3π., Wataru. Sep 22, 2014. We can find the arc length L of a polar curve r = r(θ) from θ = a to θ = b by. L = ∫ b a √r2 +( dr dθ)2 dθ. Answer link. We can find the arc length L of a polar curve r=r (theta) from theta=a to theta=b by L=int_a^bsqrt {r^2+ ( {dr}/ {d theta})^2}d theta., The arc length of a continuous curve from a to b is given by ∫ b a √1 +( dy dx)2. Let's start by computing the derivative. Now let's find the endpoints of the function y. The function y = arcsinx has domain {x ∣ − 1 ≤ x ≤ 1,x ∈ R}. However, since the value under the square root has to be positive, y = arcsin√x has domain {x ∣ ..., Find the exact length of the curve. y = 2/3 x3⁄2, 0 ≤ x ≤ 4 This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. , I need to find the exact length of the curve in the title. I'm mostly confused about how to set up y. Would y equal the square root of the other side? ... Calculate the length of the arc of the curve with an integral not involving a square root. Hot Network Questions Merge two radial shapes with clean topology, We can write the curve in parametric form by posing: x2 3 = t. so that: y2 3 = 1 − t. As in the first quadrant x and y are positive: {x = t3 2 y = (1 − t)3 2. where 0 ≤ t ≤ 1. The length of the curve is therefore: L = ∫ 1 0 √( dx dt)2 +( dy dt)2 dt.