(b) Use polar coordinates to evaluate the integral xy² dA where E is the region enclosed by the circles E centered at the origin with radius 4 and 3, the line y = x, and the y-axis in the 3rd quadrant. Sketch the region. f(x,y,z)dV where f(x,y,z)= 7x+3y and E is the rectangular box (c) Evaluate the integral E=[-4, 4] x [-4, 5] x [-5, 3]

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter7: Integration
Section7.5: The Area Between Two Curves
Problem 28E
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Question 1
(b) Use polar coordinates to evaluate the integral xy² dA where E is the region enclosed by the circles
E
centered at the origin with radius 4 and 3, the line y = x, and the y-axis in the 3rd quadrant. Sketch the
region.
(c) Evaluate the integral [f(x,y,z)dV where f(x,y,z) = 7x+3y and E is the rectangular box
E=[-4, 4] x [-4, 5] x [-5, 3]
Transcribed Image Text:Question 1 (b) Use polar coordinates to evaluate the integral xy² dA where E is the region enclosed by the circles E centered at the origin with radius 4 and 3, the line y = x, and the y-axis in the 3rd quadrant. Sketch the region. (c) Evaluate the integral [f(x,y,z)dV where f(x,y,z) = 7x+3y and E is the rectangular box E=[-4, 4] x [-4, 5] x [-5, 3]
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