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Math Help - area enclosed by cardiod.

  1. #1
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    area enclosed by cardiod.

    r = 1 + sin(theta)

    i know the integral equation should be: 1/2 integral pi/6 -> pi/2 ( 1 + sin(theta) + sin^2(theta) )

    just need help solving through the integral please.

    thanks.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Integral

    Hello rcmango
    Quote Originally Posted by rcmango View Post
    r = 1 + sin(theta)

    i know the integral equation should be: 1/2 integral pi/6 -> pi/2 ( 1 + sin(theta) + sin^2(theta) )

    just need help solving through the integral please.

    thanks.
    To integrate the \sin^2\theta term, use

    \cos 2\theta = 1 - 2\sin^2\theta

    in the form

    \sin^2\theta = \tfrac{1}{2}(1 - \cos 2\theta)

    and it's very straightforward from there.

    Grandad
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