- #1
helpm3pl3ase
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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??