math

Find the arc length of

y = ln(cos x)
over x = [0, pi/4]

  1. 👍 0
  2. 👎 0
  3. 👁 42
  1. We have to integrate sqrt[1+y'2] from 0 to pi/4

    1+y'^2 = 1+tan^2(x) = 1/cos^2(x)

    So, the arc length is:

    Integral from 0 to pi/4 of 1/cos(x)

    = Integral from pi/4 to p1/2 of 1/sin(x)


    We can write:

    1/sin(x) =

    1/[2sin(1/2 x) cos(1/2 x)] =

    [sin^2(1/2x) + cos^2(1/2x)]
    /[2sin(1/2 x) cos(1/2 x)] =


    1/2 [tan(1/2 x) + cot(1/2 x)]

    Which is trivial to integrate.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

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
  2. 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
  3. 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
  4. Calculus

    Consider the curve below. x = (cos(t))^2 y = cos(t) 0 ≤ t ≤ 6π (a) Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. (b) What is the length of the curve? I have no idea on

    asked by Jed on December 12, 2015
  5. apex geometry

    Hannah constructed two similar circles as seen in the image below. If the arc length of the larger circle is , which of the following would be true? A. The arc length of the smaller circle is proportional to the radius of the

    asked by zakiya on January 8, 2016
  6. math

    Whats the difference between an arc [of a circle]'s length and measure? And how do you find each of them? The "measure" of an arc is the angle that it subtends from the center of the circle. Call that angle A. The length of the

    asked by Emily on March 20, 2007
  7. Math rem

    2.Find the length of the arc in a circle if the radius of the circle is 24cm and the degree of the arc is 90o 3.Find the length of the arc if a circle if the degree if the arc is 120o and the length of the radius is 8cm. 4. A

    asked by bs on February 11, 2013
  8. 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].

    asked by Liz on December 19, 2012
  9. Calculus

    Find the arc length of the curve 𝑥(𝑡)=cos𝑡+𝑡sin𝑡, 0≤𝑡≤𝜋/2 𝑦(𝑡) = sin 𝑡 − 𝑡 cos 𝑡 ^2

    asked by Desperate Student on April 18, 2016
  10. Math Arc Length

    Find the arc length corresponding to an angle of a degrees on a circle radius of 4.9 Enter the exact answer. I put the arc length was 4.9api/180 got it wrong. Any help?

    asked by Taylor on October 31, 2014

More Similar Questions