Multiple Integration

**mrmaaza123** · October 21st 2012, 03:21 AM

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.

**tom@ballooncalculus** · October 21st 2012, 06:05 AM

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

... etc., hence your correct answer.

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