please help!?

Question

how do we integrate the double integral of arctan(y/x)dA, where R= {(x,y)l 1 ≤ x^2+y^2≤ 4 and 0 ≤ y ≤ x} ?

Answer 1

Use polar coordinates.

If you draw a picture of R, you'll see that it's the region corresponding to 1 <= r <= 2, and 0 <= theta <= pi/4.

Therefore, you can rewrite this integral as

integral from 1 to 2 of integral from 0 to pi/4 of
arctan(tan(theta))*r dr dtheta, or
theta*r dr dtheta.

Answer 2

Better note taking might help you