Problem $1.$ Use the method of disks$/$Washer to determine the volume of the solid obtained by rotating the region bounded by $y=x^2$ and $y=x^3$ about the $x-$axis.

Problem $2.$ Use the method of cylinders to determine the volume of the solid obtained by rotating the region bounded by $y=x^2-6x9$ and $y=-x^{2}6x-1$ about the line $x=8.$

Problem $3.$ Find the exact length of the curve $f(x)=3cosh(x)$ from $x=0$ to $x=2.$

Problem $4.$ Suppose that $x=t^2$ and $y=t^3-t.$

a$)$ Find the values of $t$ where the graph is concave up or down.

b$)$ Sketch the graph for the values of $t$ from $t=-1$ to $t=2.$ Draw an arrow on the graph to indicate the direction.

c$)$ Convert the equations from parametric form to cartesian form.