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

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) $\frac { \pi a ^ { 2 } } { 4 }$