-
Sketch the solid whose volume is given by the integral
and evaluate the integral.
-
Set up the triple integral of an arbitrary continuous function
in cylindrical or spherical coordinates over the
solid shown in the figure.
-
Evaluate ,
where is the solid that lies within the cylinder
,
above the plane ,
and below the cone .
-
Evaluate the integral
by changing to cylindrical coordinates.
-
Sketch the solid whose volume is given by the integral
and evaluate the integral.
-
Set up the triple integral of an arbitrary continuous function
in cylindrical or spherical coordinates over the
solid between the spheres
and
in all octants above the except for the first
octant. Sketch the solid.
-
Use spherical coordinates to evaluate
,
where is the region that lies above the
and below the sphere .
-
Use spherical coordinates to evaluate
,
where lies between the spheres
and
in the first octant.
-
Use spherical coordinates to evaluate
,
where is enclosed by the sphere
in the first octant.
-
Find the volume and centroid of the solid
that lies above the cone
and below the sphere .
and
-
Evaluate the integral
by changing to spherical coordinates.