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

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

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Definitions:

ATC

Stands for Average Total Cost, which is the total cost of production divided by the quantity of output produced.

AVC

Average Variable Cost, the variable cost per unit of output.

MC

Marginal Cost, the increase in cost that arises from producing one additional unit of a good or service.

Fixed Costs

Costs that do not vary with the level of production or sales, such as rent, salaries, and insurance.