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

question 309

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 solid right cylinder whose base is the region in the $x y$ -plane that lies inside the cardioid $r = 9 + 6$ cos $\theta$ and outside the circle $r = 3$ , and whose top lies in the plane $z = 8$ .

• A)
• \(\int_{0}^{\pi} \int_{3}^{9+6 \cos \theta} \int_{0}^{8} f(r, \theta, z) d z r d r d \theta\)
• B)
• \(\int_{0}^{2 \pi} \int_{3}^{9+6 \cos \theta} \int_{0}^{8} f(r, \theta, z) d z r d r d \theta\)
• C) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 9 + 6 \cos \theta } \int _ { 0 } ^ { 8 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 9 + 6 \cos \theta } \int _ { 0 } ^ { 8 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)

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