Larson_Calculus_10e ch14sec06
MULTIPLE CHOICE
1. Evaluate the following iterated integral.
a.
b.
c.
d.
e.
2. Evaluate the following iterated integral.
a.
b.
c.
d.
e.
3. Evaluate the iterated integral .
a.
b.
c.
d.
e.
4. Set up a triple integral for the volume of the solid bounded by the coordinate planes and the plane
given below.
a.
b.
c.
d.
e.
5. Set up a triple integral for the volume of the solid bounded by and .
a.
b.
c.
d.
e.
6. Set up a triple integral for the volume of the solid bounded above by the cylinder and
below by the paraboloid .
a.
b.
c.
d.
e.
7. Use a triple integral to find the volume of the solid shown below.
a.
b.
c.
d.
e.
8. Use a triple integral to find the volume of the solid shown below.
a.
b.
c.
d.
e.
9. Use a triple integral to find the volume of the solid bounded by the graphs of the equations
.
a.
b.
c.
d.
e.
10. Rewrite the iterated integral using the order .
a.
b.
c.
d.
e.
11. Sketch the solid whose volume is given by the iterated integral given below and use the sketch to
rewrite the integral using the indicated order of integration.
Rewrite the integral using the order .
a.
b.
c.
d.
e.
12. Find of the center of mass of the solid of given density bounded by the graphs of
the equations .
a.
b.
c.
d.
e.
13. Find the centroid of the solid region bounded by the graphs of the equations. Use a computer algebra
system to evaluate the triple integral. (Assume uniform density and find the center of mass.)
a.
b.
c.
d.
e.
14. Find for the indicated solid with density function .
a.
b.
c.
d.
e.
15. Set up a triple integral that gives the moment of inertia about the -axis of the solid region Q of
density given below.
a.
b.
c.
d.
e.
16. Find the center of mass of the solid bounded by and with density function
.
a.
b.
c.
d.
e.
17. Find the average value of over the region Q, where Q is a cube in the first
octant bounded by the coordinate planes, and the planes and . The average value of
a continuous function over a solid region Q is , where V is the volume
of the solid region Q.
a.
b.
c.
d.
e.
18. Find the average value of over the region Q, where Q is a tetrahedron in the first
octant with vertices and . The average value of a continuous
function over a solid region Q is , where V is the volume of the solid
region Q.
a.
b.
c.
d.
e.