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

question 137

Multiple Choice

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
-D is the rectangular solid whose base is the triangle with vertices at (0, 0) , (6, 0) , and (6, 6) , and whose top lies in the plane z = 5.

• A) \(\int _ { 0 } ^ { \pi / 4 } \int _ { 0 } ^ { 6 \csc \theta } \int _ { 0 } ^ { 5 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { \pi / 4 } \int _ { 0 } ^ { 6 \sec \theta } \int _ { 0 } ^ { 5 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 6 \csc \theta } \int _ { 0 } ^ { 5 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 6 \sec \theta } \int _ { 0 } ^ { 5 } f ( r , \theta , z ) d z r d r d \theta\)

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