A particle's velocity function is given by \( v(t) = 3t^{2} - 4t + 2 \). Find the position function if the initial position at time t=0 is 5.

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

10. \( \int_{e}^{e^{2}}\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)^{2} d x= \) (A) \( \frac{e^{4}}{2}+2 e^{2}+2 \) (B) \( \frac{e^{2}}{2}+2 e+1 \) (C) \( e^{4}+2 e^{2}+e \) (D) \( \frac{e^{4}}{2}+\frac{3 e^{2}}{2}-2 e+1 \) (E) \( \frac{e^{4}}{2}+e^{2}+e \) (Beci (B)

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

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

\( \int \frac { x + 2 } { x ( x ^ { 2 } + x + 1 ) } d x = \int \)