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 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 301

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. }
- D\mathrm { D } is the solid right cylinder whose base is the region between the circles r=7cosθr = 7 \cos \theta and r=8cosθr = 8 \cos \theta , and whose top lies in the plane z=9yz = 9 - y .


A) 02π7cosθ8cosθ09rsinθf(r,θ,z) dzrdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta
B) 0π7cosθ8cosθ09sinθf(r,θ,z) dzrdrdθ\int _ { 0 } ^ { \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } d \theta
C) 02π78cosθ09sinθcosθ(r,θ,z) dzrdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { cos } \theta ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta
D) 0π78cosθ09rsinθf(r,θ,z) dzrdrdθ\int _ { 0 } ^ { \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta

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