Sketch the Region Whose Area Is Given by the Definite $\int _ { - a } ^ { a } \sqrt { a ^ { 2 } - z ^ { 2 } } d z$

question 1

Multiple Choice

Sketch the region whose area is given by the definite integral and then use a geometric formula to evaluate the integral. $\int _ { - a } ^ { a } \sqrt { a ^ { 2 } - z ^ { 2 } } d z$

• A) \(\frac { \pi a ^ { 2 } } { 2 }\)
• B) \(\frac { \pi a ^ { 2 } } { 6 }\)
• C) \(\pi a ^ { 2 }\)
• D) \(\frac { \pi a ^ { 2 } } { 3 }\)
• E) \(\frac { \pi a ^ { 2 } } { 4 }\)

---

Definitions:

Maternal Obesity

Refers to obesity in pregnant women, which can increase the risk of complications during pregnancy and delivery.

Unborn Child

A term used to describe a fetus or embryo that is in the process of developing in the uterus and has not yet been born.

Pregnancy

The condition or period of being pregnant, where an embryo or fetus develops in a woman's uterus for about nine months.

Sudden Infant Death Syndrome (SIDS)

One type of sudden unexplained infant death whereby an infant of less than 1 year of age dies of an unexplained cause.