4. (Problem Set 34, #4) This problem is meant to refresh your memory on setting up triple integrals, since they're important in our last integral theorem. Rewrite each triple integral as an iterated integral, using whatever coordinate system you like; you need not evaluate. As a reminder, whenever you set up a triple integral not in spherical coordinates, please sketch an appropriate projection (if writing the inner integral first) or slice (if writing the outer integral first), and label the axes and any important values on your sketch. (a) x²z dV, where U is the solid enclosed by z = x² + y² and z = 8 − (x² + y²). - (b) JJJw³ sin x dV, where W consists of all points in the first octant (that is, where x, y, z are all > 0) under the plane x + 2y + 3z = 6. (Ⓒ) ¹ e dV, where is the solid enclosed by x² - 4y² + ² = 1 and the planes y = −1 and y = 1.
4. (Problem Set 34, #4) This problem is meant to refresh your memory on setting up triple integrals, since they're important in our last integral theorem. Rewrite each triple integral as an iterated integral, using whatever coordinate system you like; you need not evaluate. As a reminder, whenever you set up a triple integral not in spherical coordinates, please sketch an appropriate projection (if writing the inner integral first) or slice (if writing the outer integral first), and label the axes and any important values on your sketch. (a) x²z dV, where U is the solid enclosed by z = x² + y² and z = 8 − (x² + y²). - (b) JJJw³ sin x dV, where W consists of all points in the first octant (that is, where x, y, z are all > 0) under the plane x + 2y + 3z = 6. (Ⓒ) ¹ e dV, where is the solid enclosed by x² - 4y² + ² = 1 and the planes y = −1 and y = 1.
Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:4. (Problem Set 34, #4)
This problem is meant to refresh your memory on setting up triple integrals, since they're important in
our last integral theorem.
Rewrite each triple integral as an iterated integral, using whatever coordinate system you like; you
need not evaluate. As a reminder, whenever you set up a triple integral not in spherical coordinates,
please sketch an appropriate projection (if writing the inner integral first) or slice (if writing the outer
integral first), and label the axes and any important values on your sketch.
(a) JJJu x²z dV, where U is the solid enclosed by z = x² + y² and z = : 8 − (x² + y²).
-
(b) JJJw sin x dV, where W consists of all points in the first octant (that is, where x, y, z are all ≥ 0)
under the plane x + 2y + 3z = 6.
-1 and y
[Se
e dV, where & is the solid enclosed by x² − 4y² + z² = 1 and the planes y = −
(d) JIL e dV, where A consists of all points (x, y, z) with x² + y² + z² ≤ 9 and y ≥ x.
(c)
=
1.
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