Your integral should start off looking like and you should end up with .
I would suggest just multiplying out everything and then integrating term by term.
Could someone show me a graph of this so I can verify mine? Also, I can't figure out if I need u-substitution on this or not. I've tried to work it both ways and am not getting the correct answer.
Consider the given curves:
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis.
Given the region bounded by: .
Use the method of cylindrical shells to find the volume of the solid
obtained by rotating the region about the -axis.
We have a parabola: .
. . The vertex is and it opens to the right.
is a vertical line.
The graph looks like this:Code:| | * | * | *:::| | *::::::| | *::::::::| | (8,3)*:::::::::| | *::::::::| | *::::::| | *:::| | * | | * - - + - - - - - - - - - + - - - - - - - | 9
The curves intersect at
The formula is: .
So we have: .
. . and we must evaluate: .