Use spherical coordinates to find the volume of the solid E that
lies below the cone z = sqrt x^2 + y^2, and within the sphere x^2 +
y^2 + z^2 = 2, in the first octant.
Use spherical coordinates to evaluate the triple integral
∭e^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the region
bounded by the spheres x^2 + y^2 + z^2 = 4 and x^2 + y^2 + z^2 =
9
Evaluate the following integral,
∫
∫
S
(x2 + y2 + z2) dS,
where S is the part of the cylinder x2 +
y2 = 64 between the planes z = 0 and
z = 7, together with its top and bottom disks.
2. Assume that the potential in Cartesian coordinates is given
as V=x2-y2. According to this;
(a) The value of the potential at coordinate P (2, -1,3)
(b) Electric field, the magnitude of the displacement vector and
field lines
(c) Calculate the charge density on the conductive surface
III.) (20)
Use polar coordinates to evaluate
Dx2+y2dA
where D is the part of the disk
x2+y2=9 that
lies above the x -axis. Sketch the region of
integration.
IV.) (20) Set up a triple integral in cylindrical
coordinates to find the volume of the region above the
paraboloid
z=x2+y2 and
below the plane z=16 . (DO NOT INTEGRATE OR
EVALUATE)
V.) (20) Set up a triple integral in
spherical coordinates to find the volume of the solid
above z=0 ,...