1. Compute each of the following integrals using a technique of your choice. Then for each integral identify one other strategy that you could have attempted, and give a brief one- or two-sentence justification of why you chose your approach over the alternative. LIL. 4z dV where E is the region bounded between z = a? + y? and z = (a) 8- 22 - y? in the first octant. (b) Sey² - 4xy' ds where C is the unit circle oriented counterclockwise. Sls curlF dS where F(r, y, z) = 2²i + yj + rk and S is the triangle with (c) vertices at (1,0, 2), (0,0,3), and (2,-1,0), oriented upward. %3D SL, F. dS where F(r, y, z) = xi + yj+ 2zk and S is the outward-oriented (d) surface of the cone whose base is the unit disc in the ry-plane and whose vertex is the point (0,0, 2).
1. Compute each of the following integrals using a technique of your choice. Then for each integral identify one other strategy that you could have attempted, and give a brief one- or two-sentence justification of why you chose your approach over the alternative. LIL. 4z dV where E is the region bounded between z = a? + y? and z = (a) 8- 22 - y? in the first octant. (b) Sey² - 4xy' ds where C is the unit circle oriented counterclockwise. Sls curlF dS where F(r, y, z) = 2²i + yj + rk and S is the triangle with (c) vertices at (1,0, 2), (0,0,3), and (2,-1,0), oriented upward. %3D SL, F. dS where F(r, y, z) = xi + yj+ 2zk and S is the outward-oriented (d) surface of the cone whose base is the unit disc in the ry-plane and whose vertex is the point (0,0, 2).
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:1. Compute each of the following integrals using a technique of your choice. Then for each
integral identify one other strategy that you could have attempted, and give à brief one- or
two-sentence justification of why you chose your approach over the alternative.
Llr 4z dV where E is the region bounded between z = r? + y? and z =
(a)
8-22 - y? in the first octant.
(b)
Sey? - 4ry ds where C is the unit circle oriented counterclockwise.
Sl, curlF dS where F(r, y, z) = z²i+ yj + rk and S is the triangle with
(c)
vertices at (1,0, 2), (0,0, 3), and (2,-1,0), oriented upward.
%3D
SL F. dS where F(r, y, z) = r'i + yj+ 2zk and S is the outward-oriented
(d)
surface of the cone whose base is the unit disc in the ry-plane and whose vertex is the
point (0,0, 2).
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