Order of Integration and Show That Both Orders Yield the

Multiple Choice

$\text { The area of a region } R \text { is given by the iterated integral } \int _ { 0 } ^ { 1 } \int _ { - \sqrt { 1 - y ^ { 2 } } } ^ { \sqrt { 1 - y ^ { 2 } } } 15 d x d y \text {. Switch the }$ order of integration and show that both orders yield the same area. What is this area?

A) $\frac { 47 \pi } { 2 }$
B) $\frac { 15 \pi } { 4 }$
C) $\frac { 15 \pi } { 2 }$
D) $\frac { 31 \pi } { 4 }$
E) $\frac { 31 \pi } { 2 }$