\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 right circular cylinder whose base is the circle

\mathrm { r } = 6 \cos \theta

in the

x y - p l a n e

and whose top lies in the plane

z = 8 - x - y

.
A)

\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 \sin \theta } \int _ { 0 } ^ { 8 - \sin \theta - \cos \theta } f ( r , \theta , z ) d z r d r d \theta

\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 \cos \theta } \int _ { 0 } ^ { 8 - r ( \cos \theta + \sin \theta ) } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta

\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 6 \cos \theta } \int _ { 0 } ^ { 8 - r ( \cos \theta + \sin \theta ) } f ( r , \theta , z ) d z r d r d \theta

\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 6 \sin \theta } \int _ { 0 } ^ { 8 - \sin \theta - \cos \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta

Evaluate the Integral by Changing the Order of Integration in an Appropriate

Multiple Choice