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* (25)/(2)+ 2*\int\limits^(5)_{ (5)/(2)} { \int\limits^(√(25-(x-5)^2))_(√(25-x^2)) \, dx } \, dy \\ = \int\limits^{(\pi)/(3)}}_{- (\pi)/(3)} \int\limits^(10\ cos(\theta)) _5 {\rho} \, \ d\rho \ d\theta`

But we can make easier (see picture)