# Polar integration

1. May 13, 2004

### tandoorichicken

Find the area of the region common to $r=4\sin\theta$ and $r=4\cos\theta$

How can I find the limits of integration? I know one of the limits is pi/4 by setting r1 = r2 but I can't find the other one because it is different for each equation. The graph shows it intersecting at (0,0), but thats a different theta for each equation.

2. May 14, 2004

### HallsofIvy

Staff Emeritus
The easy way to do this is to use the symmetry. Integrate $r= 4 sin(\theta)$ for $\theta$= 0 to $\frac{\pi}{4}$, then double it.

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