Use a Computer Algebra System and the Result "The Centroid $A$

Multiple Choice

Use a computer algebra system and the result "The centroid of the region having area $A$ bounded by the simple closed path $C$ is $\bar { x } = \frac { 1 } { 2 A } \int _ { C } x ^ { 2 } d y , \bar { y } = - \frac { 1 } { 2 A } \int _ { C } y ^ { 2 } d x ^ { \prime \prime }$ to find the centroid of the region bounded by the graphs of $y = \sqrt { 196 - x ^ { 2 } }$ and $y = 0$ .

A) $\left( 0 , \frac { 56 } { 3 \pi } \right)$
B) $( 28 \pi , 0 )$
C) $( 0,56 \pi )$
D) $\left( 0 , \frac { 14 } { 3 \pi } \right)$
E) $\left( \frac { 56 } { 3 \pi } , 0 \right)$