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Help on integrating polar coordinates

  1. Jul 7, 2010 #1
    1. The problem statement, all variables and given/known data

    I was looking at the book's example. The author left the final integration as an exercise, and I was attempting it.

    1/2 integral of [ (2 - 2sin(delta) )^2 - 0 ] d delta from 0 to 2pi

    for the sake of work, i will let x = delta

    (2-2sin(x))^2 => 4 - 8sinx + 4sin^2(x)
    and i know that the half angle formula sin^2(x) = (1-cos(2x)) / 2

    rewrote:
    4 - 8*sin(x) + 2 - 2*cos(2*x)

    1/2 * integrate over x
    4x + 8*cos(x) + 2x - sin(2*x)
    and from 0 to 2pi

    1/2 [12pi + 8 - 0] - [0 - 0 - 0 -1], but the book's answer was 6pi.

    i am clueless, where is my computation error?
    thank you.
     
    Last edited: Jul 7, 2010
  2. jcsd
  3. Jul 7, 2010 #2

    Dick

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    Science Advisor
    Homework Helper

    8*cos(0)=8. The 8's cancel.
     
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