I am completely blanking on this question and I really don't even know where to start.


closed as off-topic by Leucippus, Shailesh, JMP, user91500, zhoraster Dec 15 '16 at 6:12

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  1. What do the curves look like? Sketch!
  2. Where do they intersect?
  3. What do you know about area in polar coordinates?

Solving for the point of intersection of the two curves, we get $$5\sin \theta =5\cos \theta $$ $$\Rightarrow \tan \theta =1$$ $$\Rightarrow \theta =\frac {\pi}{4} \mid \frac {5\pi}{4} $$ where $\mid $ stands for "or".

To calculate the area, we use the formula $$\frac {1}{2}\int_{a}^{b}(r_1^2-r_2^2) d\theta $$ where $a $ and $b$ are the coordinates of intersection.

Now using $r_1 = 5\sin \theta $ and $r_2 = 5\cos \theta $ and $a =\frac {\pi}{4} $ and $B =\frac {5\pi}{4} $, you shall be able to easily calculate your integral.


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