009C Sample Final 3, Problem 8

A curve is given in polar coordinates by  $r=4+3\sin \theta$

$0\leq \theta \leq 2\pi$

(a) Sketch the curve.

(b) Find the area enclosed by the curve.

Foundations:
The area under a polar curve   $r=f(\theta )$  is given by
$\int _{\alpha _{1}}^{\alpha _{2}}{\frac {1}{2}}r^{2}~d\theta$  for appropriate values of  $\alpha _{1},\alpha _{2}.$

Solution:

(a)
Insert graph

(b)

Step 1:

Step 2:

Final Answer:
(a)
(b)

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