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## Homework Statement

Evaluate the integral

∫∫R y√(x^2 + y^2) dA

with R the region {(x, y) : 1 ≤ x^2 + y^2 ≤ 2, 0 ≤ y ≤ x.}

## Homework Equations

## The Attempt at a Solution

Solution:

∫(2 to 1)∫(x to 0) y√(x^2 + y^2) dy dx

∫(2 to 1) 1/3[(x^2 + y^2)^(3/2)] |(y=x and y=0) dx

1/3 ∫(2 to 1) [(x^2 + y^2)^(3/2) - (x^2)^(3/2)] dx

1/3 x 2/5 [(x^2 + y^2)^(5/2) - (x^2)^(5/2)] |(x=2 to x=1)

final answer: 4(124√2 - 33)/15

Is this the correct answer??