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

question 211

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 = 4 cos in the xy-plane and whose top lies in the plane z = 9 - x.

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 4 \sin \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 4 \sin \theta } \int _ { 0 } ^ { 9 - r \cos \theta } f ( r , \theta , z ) d z r d r d \theta\)
• C) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 4 \cos \theta } \int _ { 0 } ^ { 9 - r \cos \theta } f ( r , \theta , z ) d z r d r d \theta\)
• D) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 4 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)

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Definitions:

Standard Deviation

A measure of the dispersion or variability around the mean of a set of data, used in finance to quantify the risk of investment returns.