Question

Use a double integral to find the area of the region. The region inside the circle (x − 2)2 + y2 = 4 and outside the circle x2 + y2 = 4

Answer 1

I agree with kiddobreeze08

Answer 2

The area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is given by

Area = ∬R dA where R is the region we're trying to find the area of.

We can find the area of the region by subtracting the area of the smaller circle from the area of the larger circle.

The area of the larger circle is:

Area = ∬R dA = ∬((x − 2)^2 + y^2 <= 4) dA = π*4 = 4π

The area of the smaller circle is:

Area = ∬((x^2 + y^2) <= 4) dA = π*4 = 4π

Therefore, the area of the region inside the circle (x − 2)^2 + y^2 = 4 and outside the circle x^2 + y^2 = 4 is

Area = 4π - 4π = 0

The area of the region is 0 square units.