Find the Coordinates of the Centroid of the Curve $x = 5 \cos t + 5 t \sin t , y = 5 \sin t - 5 t \cos t , 0 \leq t \leq \pi$

Multiple Choice

Find the coordinates of the centroid of the curve.
-Find the coordinates of the centroid of the curve $x = 5 \cos t + 5 t \sin t , y = 5 \sin t - 5 t \cos t , 0 \leq t \leq \pi$ .

A) $( \bar { x } , \bar { y } ) = \left( \frac { 60 } { \pi } - \frac { 120 } { \pi ^ { 2 } } , \frac { 120 } { \pi ^ { 2 } } - 10 \right)$
B) $( \bar { x } , \bar { y } ) = \left( 10 - \frac { 60 } { \pi } , \frac { 30 } { \pi ^ { 2 } } \right)$
C) $( \bar { x } , \bar { y } ) = \left( 10 - \frac { 120 } { \pi ^ { 2 } } , \frac { 15 } { \pi } \right)$
D) $( \bar { x } , \bar { y } ) = \left( 10 - \frac { 60 } { \pi ^ { 2 } } , \frac { 30 } { \pi } \right)$