Solve the Problem $D$ Be the Region Bounded Below by The $x y$

question 160

Multiple Choice

Solve the problem.
-Let $D$ be the region bounded below by the $x y$ -plane, on the side by the cylinder $r = 9 \sin \theta$ , and on top by the paraboloid $z = 5 r ^ { 2 }$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { dz } \mathrm { dr } \mathrm { d } \theta$ .

• A) \(\int _ { 0 } ^ { \pi / 4 } \int _ { 0 } ^ { 9 \sin \theta } \int _ { 0 } ^ { 5 r ^ { 2 } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { \pi } \int _ { 0 } ^ { 9 \sin \theta } \int _ { 0 } ^ { 5 r ^ { 2 } } r d z d r d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 9 \sin \theta } \int _ { 0 } ^ { 5 r ^ { 2 } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 9 \sin \theta } \int _ { 0 } ^ { 5 r ^ { 2 } } r d z d r d \theta\)

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