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Sine function integration

  1. Feb 12, 2014 #1
    The problem statement, all variables and given/known data

    Find the volume generated by revolving one arch of the curve y = 5 sin(x) about the x-axis.




    The attempt at a solution

    So I figured this would create a disc so I would have to use that the volume is ∏r^2 where r=sinx, r^2= (sin(x))^2 and that the way I should set this up is as shown:

    5∏∫[sin(x)]^2 from 0 to pi. And then I would replace that with the trig identities and so on. However, this is not giving me the correct answer. Is this integral wrong?
     
    Last edited: Feb 12, 2014
  2. jcsd
  3. Feb 12, 2014 #2

    Curious3141

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    Homework Helper

    r = 5sin x. You forgot to square the 5.

    And not to be pedantic, but ∏r^2 is not the volume of anything. The enclosed volume of a cylinder is ##\pi r^2h##, where h is the height. Applied here the volume integral is ##\pi\int_a^by^2dx##.
     
    Last edited: Feb 12, 2014
  4. Feb 12, 2014 #3
    Oh! Thank you so much. I did this problem a million times, and it was such a simple mistake. :)
     
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