Need Help Urgently...

Dec 2008
22
0
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 }
 
Aug 2007
318
118
Q1) By moving to polar coordinates you end up with \(\displaystyle \iint_D e^{-r^2}\cdot r\cdot drd\varphi\) where \(\displaystyle D=\left\{0\leq r \leq 2,\ -\frac{\pi}{2}\leq \varphi \leq \frac{\pi}{2}\right\}\)

The second question looks a bit strange (the limits for x).