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So we have to find the exact length of the curve. x=1+3t^2, y=4+2t^3, 0<=t<=1. y = x3 3 + 1 4x , 1 x 3 Find the exact length of the curve. $$"Length" = 59/24 approx 2.4583$$ Explanation: The formula for arclength of a function $$f(x)$$ on the interval $$(a,b)$$ is $$color(blue)(int_a^b (sqrt(1 + (f'(x))^2))dx$$. I use this formula to find it: 1 + ( d x d y) 2 d y. Question. With the information given: x = y 4 8 + 1 4 y 2, 1 y 2. 0. y = (1/3) (x + 2)/ from x = 0 to x = 3 Explanations Explanation A Explanation B Reveal next step Reveal all steps Create a free account to see explanations The y = (x/3) + x + x + 1/(4x + 4), 0 x 2 One method to measure the length of a curved line. Take a long thin thread. Take an ink pen and put some ink mark or any mark near one end of the thread. Again take the ink pen and mark the end of the curved line on the thread. Measure the distance between the two makings in the thread. It is equal to the length of the curved line. Substitute y' = (9/2)x 1/2, a = 0 and b = 1 in the above formula.. Let 81x + 4 = t 2 81dx = 2t dt dx = (2/81)t dt answered Nov 3, 2014 by casacop Expert Related questions Find the exact length of the curve analytically by antidifferentiation. Get the free "Length of a curve" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find the exact length of the curve. If the curve is parameterized by two functions x and y. r=cos^2 (/2) Post Secondary Calculus and Analysis Integral Calculus Parametric equations, polar x = y4 8 + 1 4y2 , 1 y 2. The arc length of f (x) between a and b is y = 3x 3/2 - 1 y' = 3* (3/2)x 1/2. y = 32 (1+x2)3/2, 0 x 1. Find the exact length of the curve. And take the square of this Where y between 1 and 2 okay so lets, first get it first Find the exact length of the curve. Find step-by-step Calculus solutions and your answer to the following textbook question: Find the exact length of the curve. Answer to: Find the exact length of the curve given below: y = \\sqrt{x -x^2} + \\sin^{-1} {\\sqrt x}. $ x = t \sin t $, $ \quad y = t Add To Playlist Add to Existing Playlist. How to Find the Length of the Curve? Determine the arc length of the following parametric curve. Find the exact length of the curve. Finding the Exact Length of the Curve : We need to find the length of the curve, differentiate the given {eq}y {/eq} with respect to {eq}x {/eq} for finding {eq}\frac{dy}{dx} {/eq} to evaluate the arc length of the curve. Create a New Plyalist. Showing another form of a curve $\alpha(s)$ parametrized by arc-length. Find the exact length of the curve. 478K views. y=3+1/2 coshx, 0<=x<=1 CALCULUS Find the exact length of the curve analytically by antidifferentiation. The curve equation is y = 3x 3/2 - 1 and the interval is [0, 1]. You will need to simplify the integrand algebraically before finding an antiderivative. Typo in question Find the exact length of the parametric curve(Not sure what I'm doing wrong) 1. Find the exact length of the curve analytically by antidifferentiation Homework Equations The Attempt at a Solution I use this formula right? 0. 5. x=y^4/8+1/ (4y^2) from 1 to 2. OR. The length of a curve can be determined by integrating the infinitesimal lengths of the curve over the given interval. For a function f(x), the arc length is given by s = int_{a}^{b} sqrt{ 1 + (frac{dy}{dx})^2 } dx. Enter Friends' Emails Share Cancel. Create. In this cas On the length of a curve in polar coordinates. Arc Length in Rectangular Coordinates. Let a curve C be defined by the equation y = f (x) where f is continuous on an interval [a, b]. We will assume that the derivative f '(x) is also continuous on [a, b]. Figure 1. The length of the curve from to is given by. If we use Leibniz notation for derivatives, the arc length is expressed by the formula. 3. Report Question. \ [ y=\frac {1} {4} x^ {2}-\frac {1} {2} \ln (x), \quad 1 \leq x \leq 8 \] We have an Answer from Expert View Expert Answer Expert Answer Given function Copy Link. Find step-by-step Calculus solutions and your answer to the following textbook question: Find the exact length of the curve. a curve is given by y= (9-x^ (2/3))^ (3/2) for 1 x 8. Find the exact length of the curve. y = ln 1 x2 , 0 x 1 8. Find the exact length of the parametric curve $(x,y)=(\theta+ Stack Exchange Network. Use a graph to determine the parameter interval. arc\:length\:x,\:0,\:1; arc\:length\:\sqrt{1-x^{2}} arc\:length\:\ln(\sec(x)),\:[0,\:\frac{\pi}{4}] arc\:length\:y=2x^{2}+3,\:0\le x\le 1 Find the exact length of the curve. Find the exact length of the curve. y = 2/3 x32, 0 x 4. Find an equation of the following curve in polar coordinates and describe the curve. Find the exact length of the curve. How to Calculate the Length of a Curve The formula for calculating the length of a curve is given as: L = a b 1 + ( d y d x) 2 d x Where L is the length of the function y = f (x) on the x interval [a, x = e t + e t, y = 5 2 t, 0 t 3 Ask Expert 2 See Answers You can still ask an expert for help Expert Answer Lounctirough Answered 2021-11-20 Author has 14 answers x = e t + e t, y = 5 2 t, 0 t 3 We know that the length L of a curve L = a b ( d x d t) 2 + ( d y d t) 2 d t Okay, so the exact length of the curve and the curve is given if x, is equals to y, raise to the power 4 divided by 8 plus 1 by 4 y square. The general formula is given by, Find the exact length of the curve. Parameterized Function:. So we have a formula for the length of the curve which is from a to b integral squared off one plus after V. Two X. Find the exact length of the curve. y=1-e^-x, 0<=x<=2. Find more Mathematics widgets in Wolfram|Alpha. I must find the exact length of the curve. Add to playlist. Summary: The exact length of the polar curve r = 2, 0 is 1 3[(2 +4)3 2 8] 1 3 [ ( 2 + 4) 3 2 8]. 0 t 2 So of course, I should find what 1 + Explicit Curve y = f (x):. Stack Exchange network consists of 182 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. x = y4 8 +. 1) Find the exact length of the curve: y = 3 2 x 3/2 0 x 4 2) Find the arc length function for the curve y = 2 x 3/2 With starting point P 0 (4, 16) Previous question Next question Get more help from Chegg Share Question. You will need to simplify the integrand algebraically before finding an antiderivative. OR. x = ( 1 + cos t ) cos t y = ( 1 + cos t ) sin t . y = 1 + 6x^ 3/2 0 <=x<= 1 CALCULUS Find the exact length of the curve. The formula which is used to measure the length of the arc will be:Arc Length Formula, when is in degrees then s = 2 r (/360)Arc Length Formula when is in radius then s = X rArc Length Formula which is in Integral Form = s= ba1+ (dydx)2dxab1+ (dydx)2dx The exact length of the curve, y = x 3 /3 + 1/4x , 1 x 3 is 53/6.