$($calculator$)$ Let $f(t)={\displaystyle \underset{-t}{\overset{t}{}}}cos2xdx.$

a$.$ Approximate $f(3)$ using a trapezoidal rule with $2$ equal subintervals.

b$.$ Find the average value of $cos2x$ on the interval $-3,3$

c$.$ Find all values of $t$ on the interval $0,3$ where $f$ has a critical point.

d$.$ Find all values of $t$ on the interval $0,3$ where $f$ has a point of inflection.

e$.g(t)*f(t)=2$ when $g^{\text{'}}(1)y=cos2xy=(x-1{)}^{2}x0.$ Find $g^{\text{'}}(1).$

$f.$ Find the area $of$ the region bounded between $y=cos2x$ and $y=(x-1{)}^2.$

$g.$ Find the volume $of$ the solid generated $by$ revolving the region $in$ question $(f)$ about the $x-$axis.