Solved

 Set up the iterated integral for evaluating Df(r,θ,z)dzrdrdθ over the given region D. \text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }

Question 320

Multiple Choice

 Set up the iterated integral for evaluating Df(r,θ,z) dzrdrdθ over the given region D. \text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }
- DD is the solid right cylinder whose base is the region in the xyx y -plane that lies inside the cardioid r=9+6r = 9 + 6 cos θ\theta and outside the circle r=3r = 3 , and whose top lies in the plane z=8z = 8 .


A)
0π39+6cosθ08f(r,θ,z) dzrdrdθ\int_{0}^{\pi} \int_{3}^{9+6 \cos \theta} \int_{0}^{8} f(r, \theta, z) d z r d r d \theta

B)
02π39+6cosθ08f(r,θ,z) dzrdrdθ\int_{0}^{2 \pi} \int_{3}^{9+6 \cos \theta} \int_{0}^{8} f(r, \theta, z) d z r d r d \theta

C) 0π09+6cosθ08f(r,θ,z) dzrdrdθ\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 9 + 6 \cos \theta } \int _ { 0 } ^ { 8 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta

D) 02π09+6cosθ08f(r,θ,z) dzrdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 9 + 6 \cos \theta } \int _ { 0 } ^ { 8 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta

Correct Answer:

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