Question

The bounded area by the graph y=sqrt(x), y=x-4 and the x axis is rotated along the x axis to form a solid. Use Integration By Shells to find the Volume of the Solid.

Answer 1

This might help utilize the "Shell" method; https://www.khanacademy.org/math/integral-calculus/solid_revolution_topic/solid_of_revolution/v/solid-of-revolution-part-5

Answer 2

This is the bounded area

Answer 3

Wait so how does the integral change when you rotate it around the x axis instead of y?

Answer 4

https://www.wyzant.com/resources/lessons/math/calculus/integration/finding_volume

Answer 5

With "washer method"

Answer 6

To rotate about the y-axis, swap the roles of x and y throughout the
above discussion. To rotate about a different axis, change
coordinates so that the axis of rotation is one of the coordinate
axes, and then do the computation.

Answer 7

Follow rules of "shell" and "washer" method to guide throughout finding volume

Answer 8

been a while, and I was never great at these so take this with a grain of salt. I believe you have to change the formulas around and integrate in terms of y.