Question

Evaluate the double integral y^2/(x^2+y^2)dA, where R is the annular region bounded by the circles x^2+y^2=1 and x^2+y^2=2.

Answer 1

familiar with double integrals in polar coordinates ?

Answer 2

There is a Explaination for this and it is awesome

Answer 3

Yes.

Answer 4

Rewrite in terms of r.

x = rcos(theta)
y = rsin(theta)
x^2 + y^2 = r^2

Answer 5

Instead of x and y, your two integrals will be the radius and the angle.
Your radius in this equation goes from 1 to 2.

Answer 6

Your angle of rotation is from 0 to 2Pi.

So the bounds for your double integral will be:
dr = 1 to 2
dtheta = 0 to 2pi

Answer 7

Simple integration from there.