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Stewart_Calc_7ET ch15sec07
MULTIPLE CHOICE
1. Calculate the iterated integral.
a.
8
b.
c.
d.
e.
None of these
2. Use a triple integral to find the volume of the solid bounded by and the planes
and .
a.
b.
c.
d.
e.
3. Evaluate the integral where and
with respect to x, y, and z, in that order.
a.
120
b.
620
c.
180
d.
500
8
3
4. Find the mass of the solid S bounded by the paraboloid and the plane if
S has constant density 3.
a.
16.25
b.
15.07
c.
24.91
d.
13.92
e.
19.63
NUMERIC RESPONSE
1. Express the volume of the wedge in the first octant that is cut from the cylinder
by the planes and as an iterated integral with respect to , then to , then to .
2. The joint density function for a pair of random variables and is given.
Find the value of the constant .
3. Evaluate the triple integral. Round your answer to one decimal place.
lies under the plane and above the region in the -plane bounded by the
curves , and .
4. Evaluate the triple integral. Round your answer to one decimal place.
5. Express the integral as an iterated integral of the form where E is
the solid bounded by the surfaces
6. Find the mass of the solid E, if E is the cube given by and the
density function is .
7. Find the moment of inertia about the y-axis for a cube of constant density 3 and side length
if one vertex is located at the origin and three edges lie along the coordinate axes.
SHORT ANSWER
1. Evaluate the iterated integral
2. Express the triple integral as an iterated integral in six different ways
using different orders of integration where T is the solid bounded by the planes
and
3. Sketch the solid bounded by the graphs of the equations and ,
and then use a triple integral to find the volume of the solid.
4. Sketch the solid whose volume is given by the iterated integral
5. Set up, but do not evaluate, the iterated integral giving the mass of the solid T bounded by
the cylinder in the first octant and the plane having mass density
given by
6. Sketch the solid whose volume is given by the integral
Evaluate the integral.
