Consider the region in the $xy-$plane bounded by the functions

$f(x)=16x$ and $g(x)=4x^2$

Analysis

Draw the bounded region in the first quadrant and include an approximating rectangle across the region depending on your method of choice. Additionally, include the axis of rotation and identify the two functions.

Inquiry

$2.$ Write a definite integral that gives the volume of revolution of the region about the line $=4.$

#$3.$ Use the information given in the problem to find the volume that results from rotating the bounded region about the line $x=4.$ Show all steps clearly

#$4.$ Write a conclusion that explains your method of choice.