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Math Help - Multiple Integration

  1. #1
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    Multiple Integration

    This question is regarding finding the area under a polar curve using double integrals in polar coordinates.
    The question goes like this:

    Find the area of the region bounded by the cardiod, r = 1+sin(theta) ?

    I have attempted the question and my answer is coming out to be 3pi/2. Is it correct ?
    Also please do specify the limits to be taken for theta .

    Please use double integrals in polar coordinates.

    Help will be appreciated.
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  2. #2
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    Re: Multiple Integration

    \begin{align*} \int_0^{2\pi}\ \int_0^{1 + \sin \theta}\ r\ dr\ d\theta\ &=\ \int_0^{2\pi}\ [\tfrac{1}{2} r^2]_0^{1 + \sin \theta}\ d\theta \\ \\ &= \tfrac{1}{2}\ \int_0^{2\pi}\ (1 + \sin \theta)^2\ d\theta  \end{align*}

    ... etc., hence your correct answer.
    Thanks from mrmaaza123
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