calc arc length

Find the length of the arc along f(x) = integral from 0 to x^3 sqrt(cos t) dt on the set of x [0, pi/3].

1. 👍 0
2. 👎 0
3. 👁 47
1. You need to integrate sqrt[1+f'(x)^2] from x = 0 to pi/3. Computing the derivative of f(x) is not difficult, you can use the chain rule, substitute u = x^3 for the upper limit and use that the derivative w.r.t. x is the derivative w.r.t u times the derivative of of u w.r.t. x. The derivative w.r.t. u is, by the Fundamental Theorem of Calculus, equal to sqrt[cos(u)].

1. 👍 0
2. 👎 0

Similar Questions

1. AP Calc B/C

Find the arc length of one arch of the sine curve. I started it by doing y=sinx, y'=cosx arc length= integral of sqrt(1+cos^2x)dx from pi/2 to 3pi/2 but I don't know how to integrate that! Thank you!

asked by Anon on September 13, 2014

I'm having trouble with this question on arc length: y=lnx, (squareroot)3/3 greater than or equal to x less than or equal to 1 It sounds as if you want the length of the y = ln x curve from x = sqrt(3)/3 (0.57735..) to 1. The

asked by Krystal on October 19, 2006
3. calculus

Find the length of the arc formed by y = (1/8)(4x^2-2ln(x)) from x=4 to x=8. I found the derivative of the function and got y'= x-(1/4x) Where I'm lost now is after plugging it into the arc length equation: integral of

asked by Arc Length on August 24, 2008
4. calc

find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the

asked by mikayla on April 18, 2007
5. calculus

Find the length of the curve given by the equation y= intergral from -pi to x of sqrt(cos(t)) dt for x between -pi and pi. I think I know to do this- at least part of it. I am using the fundamental theorem of calculus and the arc

asked by Dean on August 2, 2017
6. calc: arc length

Posted by COFFEE on Monday, June 11, 2007 at 11:48pm. find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2

asked by COFFEE on June 12, 2007
7. Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilateral triangles. for y=x^2,

asked by Anonymous on December 15, 2007
8. Calculus

I know how to do this problem, but I'm stuck at the arc length differential. Set up an integral for the arc length of the curve. (Do not evaluate the integral) x=y^2ln(y), 1

asked by Angie on February 28, 2013
9. Calculus

Find the equation of the curve that passes through the point (x, y) = (0, 0) and has an arc length on the interval 0⩽x⩽π/4 given by the integral from 0 to π/4 of√(1+cos^2x) dx. a) y= sin(x) ------> My answer. Can you check

asked by Alice on May 8, 2019
10. Calc II

For the following question, we need to find the length of the polar curve: r= 2/(1-cosx) from pi/2

asked by Jenna on December 13, 2009

More Similar Questions