Q1) By moving to polar coordinates you end up with where
The second question looks a bit strange (the limits for x).
Q1 - Evaluate the iterated integral by converting to polar coordinates
∫0 to 2 ∫-Sqrt 4-x^2 to Sqrt 4-x^2 e^(-x^2-y^2) dy dx
The region of integration is bounded by
-Sqrt 4-x^2 ≤ y ≤ Sqrt 4-x^2 and 0 ≤ x ≤ 2
Q2 - Evaluate the triple integral ∫∫R∫ OR ∫∫∫R f(x,y,z)dV
With f(x,y,z)=Sqrt y -3z^2
Q = {(x,y,z)/2 ≤ x ≤ 3, 0≤ y ≤1, -1≤ z ≤1 }