MATH 210
Homework due 03/05/2012
1. Let Rbe the circle centered at the origin with radius 3. Compute the
integral:
ZZR
(x2+y2)3/2dA
2. Let Rbe the part of annulus with radii 1 and 3 centered at the origin,
which corresponds to angles between π/2 and π. Compute the integral
ZZR
x dA.
3. Evaluate ZZD
x2dA where Dis the region in the first quadrant which
is enclosed by the curve defined by the equation r2= sin(2θ).
4. Find the volume of the solid between the hyperboloid
z= 3 −p1 + x2+y2
and the region
{(x, y) : x2+y2≤1, y > 0}
in the xy plane.
5. Compute the integral ZZR
dA
x2+y2+ 1 where
R={(x, y) : 1 < x2+y2<4, x > 0, y < 0}
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