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.
Find the area enclosed by the loop $r=2(1-\sin\theta)\sqrt{\cos\theta}$
4
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calculus
trigonometry
polar-coordinates
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5a) 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