Surgent MAT 267 ONLINE A Spring 2019
Assignment Midterm 3 due 02/11/2019 MST
Problem 1.
1. (1 point)
Match each double integral in polar with the graph of
the region of integration.
? 1. Z3π/4
−π/4Z4
3
f(r,θ)r dr dθ
? 2. Z3
0Z3π/4
0
f(r,θ)r dθdr
? 3. Z2π
0Z4
3
f(r,θ)r dr dθ
? 4. Z3π/2
3π/4Z3
0
f(r,θ)r dr dθ
? 5. Z2π
0Z3
0
f(r,θ)r dr dθ
? 6. Z4
3Z7π/4
3π/4
f(r,θ)r dθdr
? 7. Z2π
3π/2Z4
0
f(r,θ)r dr dθ
? 8. Z3
0Z3π/4
−π/2
f(r,θ)r dθdr
A B C
D E F
G H
Answer(s) submitted:
•A
•C
•E
•F
•D
•H
•B
•G
(correct)
Problem 2.
2. (1 point)
Convert the integral below to polar coordinates and evaluate
the integral.
Z4/√2
0Z√16−y2
y
xy dx dy
Instructions: Please enter the integrand in the first answer box,
typing theta for θ. Depending on the order of integration you
choose, enter dr and dtheta in either order into the second and
third answer boxes with only one dr or dtheta in each box.
Then, enter the limits of integration and evaluate the integral to
find the volume.
ZB
AZD
C
A =
B =
C =
D =
Volume =
Answer(s) submitted:
•rcos(theta)rsin(theta)r
•16
(correct)
Problem 3.
3. (1 point) Find the volume of the solid enclosed by the
paraboloids z=9x2+y2and z=18 −9x2+y2.
Answer(s) submitted:
•9/pi
(incorrect)
Problem 4.
4. (1 point) Evaluate the triple integral
ZZZE
xy dV where Eis the solid tetrahedon with vertices
(0,0,0),(10,0,0),(0,5,0),(0,0,6).
Answer(s) submitted:
•125
(correct)
1
Problem 5.
5. (1 point) Suppose f(x,y,z) = x2+y2+z2and Wis the
solid cylinder with height 7 and base radius 2 that is centered
about the z-axis with its base at z=−2. Enter θas theta.
(a) As an iterated integral,
ZZZ
W
f dV =ZB
AZD
CZF
E
dz dr dθ
with limits of integration
A =
B =
C =
D =
E =
F =
(b) Evaluate the integral.
Answer(s) submitted:
•(rˆ2+zˆ2)r
•0
•2pi
•0
•2
•-2
•5
•700pi/3
(correct)
Problem 6.
6. (1 point) Express the point given in Cartesian coordinates
in cylindrical coordinates (r,θ,z).
A) 71
2,7√3
2,−7=( , , )
B)−71
2,7√3
2,−7=(, , )
C)71
2,−7√3
2,−7=(, , )
D)−71
2,−7√3
2,−7=(, , )
Answer(s) submitted:
•sqrt((7(1/2))ˆ(2)+(7(sqrt(3)/2))ˆ(2))
•tanˆ(-1)((7(sqrt(3)/2))/(7(1/2)))
•-7
•sqrt((7(1/2))ˆ(2)+(7(sqrt(3)/2))ˆ(2))
•2pi/3
•-7
•sqrt((7(1/2))ˆ(2)+(7(sqrt(3)/2))ˆ(2))
•tanˆ(-1)((-7(sqrt(3)/2))/(7(1/2)))
•-7
•sqrt((7(1/2))ˆ(2)+(7(sqrt(3)/2))ˆ(2))
•4pi/3
•-7
(correct)
Problem 7.
7. (1 point) Evaluate the integral.
Z3
0Z√9−x2
−√9−x2Z√9−x2−z2
−√9−x2−z2
1
(x2+y2+z2)1/2dydzdx =
Answer(s) submitted:
•28.2743
(correct)
Problem 8.
8. (1 point) Evaluate the iterated integral R4
0R2
04x2y3dxdy
Answer(s) submitted:
•2048/3
(correct)
Problem 9.
9. (1 point) Evaluate the integral by reversing the order of
integration.
Z1
0Z6
6y
ex2dxdy =
Answer(s) submitted:
•3.59269*10ˆ(14)
(correct)
Generated by c
WeBWorK, http://webwork.maa.org, Mathematical Association of America
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