An Object in Rectilinear Motion Is Moving Along a Horizontal $v ( t ) = \sin ^ { 3 } ( t )$

Multiple Choice

An object in rectilinear motion is moving along a horizontal line with velocity $v ( t ) = \sin ^ { 3 } ( t )$ m/s for the time interval $0 \leq t \leq \frac { 3 \pi } { 4 }$ seconds. What is the net displacement from t = 0 to $t = \frac { 3 \pi } { 4 }$ ?

A) $\int _ { \pi / 4 } ^ { \pi } - 5 \cos ^ { 4 } ( t ) \sin ( t ) d t$
B) $\int _ { \pi / 4 } ^ { \pi } \left| 5 \cos ^ { 4 } ( t ) \sin ( t ) \right| d t$
C) $\int _ { \pi / 4 } ^ { \pi } \left| \cos ^ { 5 } ( t ) \right| d t$
D) $\int _ { \pi / 4 } ^ { \pi } \sqrt { 1 + \left( \cos ^ { 5 } ( t ) \right) ^ { 2 } } d t$
E) $\int _ { \pi / 4 } ^ { \pi } \cos ^ { 5 } ( t ) d t$