Mathematica Activity $(3$ points$)$

Name:

$($due Thursday, July $10,2025)$

Let $f(x)=x^{2}3x$ and $g(x)=x8.$ Use Mathematica to do the following.

a$.$ Find the $x-$values where the two functions intersect.

b$.$ Plot the two functions on the same set of axes.

c$.$ Find the area bounded by the two curves

d$.$ Find the volume when the bounded area is revolved about the line $y=-4.$

e$.$ Find the volume when the bounded area is revolved about the line $x=2.$