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Thread: area of parametric curve?

  1. #1
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    area of parametric curve?

    area of parametric curve?-capture.png

    I keep getting 0 for the area?

    dy/dt = 36sin^2t
    dx/dt = 36(1-cost)^2

    integral from 0 -> 2pi of sqrt(36sin^2t + 36(1-cost)^2)

    = integral 6sqrt(2) sqrt(1-cost) from 0-->2pi = 6sqrt(2) u^-1/2 = 0??
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  2. #2
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    Re: area of parametric curve?

    area of parametric curve?-clipboard01.jpg
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    Re: area of parametric curve?

    Quote Originally Posted by lc99 View Post
    Click image for larger version. 

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    I keep getting 0 for the area?

    dy/dt = 36sin^2t
    dx/dt = 36(1-cost)^2
    Where are the 36's coming from? Also the derivatives don't have any squares in them.

    integral from 0 -> 2pi of sqrt(36sin^2t + 36(1-cost)^2)

    = integral 6sqrt(2) sqrt(1-cost) from 0-->2pi = 6sqrt(2) u^-1/2 = 0??
    For rotation about the x axis you need a $2\pi y$ factor.
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  4. #4
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    Re: area of parametric curve?

    I have taken the limits from 0 to pi/2 according to your Question.









    You can do this integral easily without calculator, but it will be a little long. I will give you the answer directly to shorten the time!

    Last edited by joshuaa; Apr 27th 2018 at 03:06 PM.
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