Evaluate the Double Integral Below $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 5 + 5 \sin \theta } \theta r d r d \theta$

question 16

Multiple Choice

Evaluate the double integral below. $\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { 5 + 5 \sin \theta } \theta r d r d \theta$

• A) \(\frac { 225 } { 8 } + \frac { 5 } { 16 } \pi ^ { 2 }\)
• B) \(\frac { 225 } { 16 } + \frac { 75 } { 32 } \pi ^ { 2 }\)
• C) \(\frac { 225 } { 8 } + \frac { 75 } { 32 } \pi ^ { 2 }\)
• D) \(\frac { 225 } { 8 } + \frac { 75 } { 32 } \pi\)
• E) \(\frac { 5 } { 8 } + \frac { 5 } { 32 } \pi\)

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Definitions:

Central Nervous System

The part of the nervous system consisting of the brain and spinal cord, which coordinates and controls body activities.

Conception

The process of fertilization where a sperm combines with an egg to form a zygote.

Birth

The process of childbirth; marking the emergence of a baby from the mother's womb into the world.

Germinal Period

The period in prenatal development from conception to two weeks after conception, when the zygote divides rapidly and implants in the uterine wall.