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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Definitions:

Neurons

Specialized cells within the nervous system that transmit information to other neurons, muscles, or gland cells.

Muscle Tissue

A tissue composed of cells or fibers, the function of which is to contract to facilitate movement of the body or its parts.

Contractility

The ability of muscle fibers to shorten and generate force.

Glia

Non-neuronal cells in the central and peripheral nervous system that support, nourish, and protect neurons.