Question

Find the area of the smaller loop r=2-4sin0, symmetrical with Oy.

Answer 1

We know,

Area can be evaluated as $\int rd \theta$

We have given that $r = 2-4sin\theta$

Hence $I = \int_{0}^{2\pi} (2-4sin\theta) d\theta$

$I = [_{0}^{2\pi} (2\theta+4cos\theta)$

We get $I = 4\pi + 4 - 0 - 4$

Hence, $I = 4\pi$