4. Suppose you are using a triple integral to find the volume of the region contained between the paraboloids z = x² + y² and z = 8-2² - y². Which of the following is a valid setup for your triple integral? (a) -2 LLL (b) (c) (d) LLE (a) (c) do 1 (b) dz dy da -x2 (e) None of the other choices. 5. Which of the following is a valid setup for a triple integral that gives the mass of the tetrahedron whose vertices are (0, 0, 0), (1, 0, 0), (0, 1,0), and (0, 0, 1), supposing that the density function for the region is p(x, y, z)? -1-z Г.Г dz dy dx √4-2² 8-x²-y² √4-x² dz dy dz -1-z 1-y-z Jo dz dy da 1-z-y *** p(x, y, z) dz dy dx. p(x, y, z) dx dy dz. 1-z 1-z-z ²²*¹** p(x, y, z) dy dz da. Jo (d) All of (a), (b), and (c). (e) None of the other choices.
4. Suppose you are using a triple integral to find the volume of the region contained between the paraboloids z = x² + y² and z = 8-2² - y². Which of the following is a valid setup for your triple integral? (a) -2 LLL (b) (c) (d) LLE (a) (c) do 1 (b) dz dy da -x2 (e) None of the other choices. 5. Which of the following is a valid setup for a triple integral that gives the mass of the tetrahedron whose vertices are (0, 0, 0), (1, 0, 0), (0, 1,0), and (0, 0, 1), supposing that the density function for the region is p(x, y, z)? -1-z Г.Г dz dy dx √4-2² 8-x²-y² √4-x² dz dy dz -1-z 1-y-z Jo dz dy da 1-z-y *** p(x, y, z) dz dy dx. p(x, y, z) dx dy dz. 1-z 1-z-z ²²*¹** p(x, y, z) dy dz da. Jo (d) All of (a), (b), and (c). (e) None of the other choices.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. Suppose you are using a triple integral to find the volume of the region contained
between the paraboloids z = x² + y² and z = 8-2² - y². Which of the following is
a valid setup for your triple integral?
(a)
-2
LLL
(b)
(c)
(d)
LLE
(a)
(c)
do 1
(b)
dz dy da
-x2
(e) None of the other choices.
5. Which of the following is a valid setup for a triple integral that gives the mass of the
tetrahedron whose vertices are (0, 0, 0), (1, 0, 0), (0, 1,0), and (0, 0, 1), supposing that
the density function for the region is p(x, y, z)?
-1-z
Г.Г
dz dy dx
√4-2² 8-x²-y²
√4-x²
dz dy dz
-1-z 1-y-z
Jo
dz dy da
1-z-y
*** p(x, y, z) dz dy dx.
p(x, y, z) dx dy dz.
1-z
1-z-z
²²*¹** p(x, y, z) dy dz da.
Jo
(d) All of (a), (b), and (c).
(e) None of the other choices.
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