Question

Use a double integral to find the area of the region. the region inside the circle (x − 5)^2 y^2 = 25 and outside the circle x^2 y^2 = 25 which one is the inside integral and how do i find the bounds for it. is x=r, or is x=rcos(theta)? i'm confused.

Answer 1

Hello,

I have search in my memory : (not sure)

$A= \pi* \dfrac{25}{2}+ 2*\int\limits^{5}_{ \frac{5}{2}} { \int\limits^{\sqrt{25-(x-5)^2}}_{\sqrt{25-x^2}} \, dx } \, dy \\ = \int\limits^{\frac{\pi}{3}}}_{- \frac{\pi}{3}} \int\limits^{10\ cos(\theta)} _5 {\rho} \, \ d\rho \ d\theta$

But we can make easier (see picture)