El área bajo la curva representa la distancia recorrida por e

\( = \int _ { 0 } \frac { \partial t } { 1 + t ^ { 3 } } \)

seconds, is given by \( a(t)=t+1 \). Given that \( s=0 \) and \( v=8 \) when \( t=0 \), find formula for: (a) The velocity \( v \) (b) The displacement

\( F ( x ) = \int _ { 0 } ^ { \sin x } \frac { d t } { 1 + t ^ { 3 } } \)

5) A particle is moving in a straight line with velocity \( v(t)=15 t^{2}+2 \). Find; a) Its acceleration after 3 seconds b) Its displacement after 2 secnds

Determine the area bounded by the functions \( y = \sin(x) \) and \( y = \cos(x) \) within the interval \( [0, \frac{\pi}{2}] \).