ASSIGNMENT 2
(EE1 AND EE22)
1.
Find the volume of the region T lying between the sphere = 3 (in spherical
coordinates) and the cone = =6.
2.
Find the integral of the function
f(x; y) = x2
yz
over the region lying under the graph of the function...
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ASSIGNMENT 2
(EE1 AND EE22)
1.
Find the volume of the region T lying between the sphere = 3 (in spherical
coordinates) and the cone = =6.
2.
Find the integral of the function
f(x; y) = x2
yz
over the region lying under the graph of the function z = x2
and over the
region in the x y plane with x2
+ y2
4 and y 0 .
3.
Find the volume of the region lying under the graph of the function
f(x; y) = cos(x2
+ y2
) + 1
which lies over the circle of radius 3 in the x y plane centered at the
origin.
4.
Convert the following integrals to equivalent itegrals in rectangular coordinates after sketching the regions
=2R
0
p
3R
1
p
4 r2
R
1
r3
sin 2 z2
dzdrd :
5.
Find the moment of inertia about z-axis of a solid of constant density = 3;
which is bounded above by the sphere of radius 2 about the origin and below
by the cone ? = 4
:
1
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