Check your limits for the shells
I have the function f(x)=x2
I am to give the volume of the shape when this function is spun 360 degrees around the x axis by using the disc method, and the shell method, from x=1 and x=3.
When I work out the disc method, I get (242pi)/5. But when I use the shell method, I get (232pi)/5. I have been looking over my work, and it all seems to work out, so I am curious why they are different. I will show my setups below:
Then I integrate and get that v=pi[(1/5)x5]31 which gives me (242pi)/5.
I then integrate, and get that v=2pi[(3/2)y2-(2/5)y5/2]91 which then gives me (232pi)/5.
Have I done something wrong here? Or is there a reason for the discrepancy?
Hint: Currently, you are finding the volume of a shape that has a cylindrical hole through the center.