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

question 23

Multiple Choice

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
- $\mathrm { D }$ is the solid right cylinder whose base is the region in the xy-plane that lies inside the cardioid $r = 6 - 2$ sin $\theta$ and outside the circle $r = 4$ , and whose top lies in the plane $z = 10$ .

• A) \(\int_{0}^{\pi} \int_{4}^{6-2 \sin \theta} \int_{0}^{10} \mathrm{f}(\mathrm{r}, \theta, \mathrm{z}) \mathrm{dz} \mathrm{rdr} \mathrm{d} \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 4 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } \mathrm { f } ( \mathrm { r } , \theta , z ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } f ( r , \theta , z ) d z r d r d \theta\)
• D) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 6 - 2 \sin \theta } \int _ { 0 } ^ { 10 } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } \mathrm { d } \theta\)

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