$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
-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) $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 6 \sec \theta } \int _ { 0 } ^ { 5 } f ( r , \theta , z ) d z r d r d \theta$

Question

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
-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) $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 6 \sec \theta } \int _ { 0 } ^ { 5 } f ( r , \theta , z ) d z r d r d \theta$

Quizplus · Accepted Answer

The Answer of $$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
-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) $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 6 \sec \theta } \int _ { 0 } ^ { 5 } f ( r , \theta , z ) d z r d r d \theta$