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

question 384

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 right circular cylinder whose base is the circle $r = 8 \sin \theta$ in the xy-plane and whose top lies in the plane $z = 10 - y$ .

• A) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 8 \sin \theta } \int _ { 0 } ^ { 10 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 8 \sin \theta } \int _ { 0 } ^ { 10 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 8 \sin \theta } \int _ { 0 } ^ { 10 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { r } \mathrm { dr } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 8 \sin \theta } \int _ { 0 } ^ { 10 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)

---

Definitions:

Sample Means

The average value of a set of measurements or quantities taken from a larger population, used as an estimate of the overall population mean.

Sampling Distribution

The likelihood distribution for a particular statistic derived from a random sample, utilized for estimating the population parameter.

Sample Proportion

The fraction of members in a sample that have a particular attribute.

Population Proportion

The fraction or percentage of members in a population that possess a particular attribute or characteristic.