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The diagram shows a sketch of the loop whose polar equation is

$$r=2(1-\sin\theta),\qquad -\frac{\pi}{2}\leq\theta\leq\frac{\pi}{2}$$

a)Show that the area enclosed by the loop is 16/3.

b)Show that the initial line divides the area enclosed by the loop in the ratio 1:7.

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    a) Integrate $\frac12r^2d\theta$, with $\theta$ running over $-\frac{\pi}2$ to $\frac{\pi}2\\$ b) Integrate the same from $\frac{-\pi}2$ to $0$ and see to it, that the answer is $\frac78$ times that you got in a)2012-07-11

2 Answers 2