Evaluate the Triple Integral $\iiint _ { E } r d V$

question 261

Multiple Choice

Evaluate the triple integral $\iiint _ { E } r d V$ in cylindrical coordinates, where $E = \{ ( r , \theta , z ) \mid 0 \leq r \leq 1,0 \leq \theta \leq 2 \pi , 0 \leq z \leq 1 \}$ .

• A) \(\frac { \pi } { 4 }\)
• B) \(\frac { \pi } { 3 }\)
• C) \(\frac { \pi } { 2 }\)
• D) \(\frac { 2 \pi } { 3 }\)
• E) \(\frac { 3 \pi } { 4 }\)
• F)\(\pi\)
• G) \(\frac { 4 \pi } { 3 }\)
• H)2\(\pi\)

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Definitions:

Insulin

A hormone produced by the pancreas that regulates blood glucose levels by facilitating the uptake of glucose into tissues, used medically to treat diabetes.

Quantity Demanded

The total amount of a good or service that consumers are willing to buy at a given price level in a given period.

Perfectly Inelastic

Describing a situation where the quantity demanded or supplied of a good does not change in response to a price change.

Demand Curve

A graphical representation of the quantity of a good that consumers are willing and able to purchase at various prices during a given period.