\( y ^ { \prime \prime } + y = 2 \quad y ( 0 ) = 0 \quad y ^ { \prime } ( 0 ) = 1 \)

Determine the extreme values of the function \( f(x)=e^{\text {arcsinit }} \) for \( -1 \leqslant x \leqslant 1 \)

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

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

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

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