Volume of Revolution/Integration by Parts problem

[ahsanxr]

Homework Statement

Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y=e^x and the line x=ln13 about the line x=ln13.

Homework Equations

The Attempt at a Solution

I'm not really sure as to how to do this problem as the only volume of revolution techniques I know are rotating a curve about the x-axis and y-axis. I do not know how to find the volume of revolution involving a curve and a line or two different curves and rotating them about a line other other than the axes. So with the aid of examples, someone please help me solve this type of problem.

 

[rootX]

You can always shift the center to the left so that you are revolving at x=0 You should draw the picture and then imagine that you are rotating about x=0 rather than x=ln13

 

[ahsanxr]

Won't that give a different volume? (at least for this particular problem)

 

[rootX]

Won't that give a different volume?

Why would it? Try to visualize the problem. Shifting the centers does not change the volume if you properly shift all the functions involved so that you see same object when it is revolved around.

 

[ahsanxr]

Oh I misinterpreted what you said. I get what you're saying now but still don't understand how that will help me solve the problem. If I shift the curves then won't that change the original equation of the curve?

 

[rootX]

Oh I misinterpreted what you said. I get what you're saying now but still don't understand how that will help me solve the problem. If I shift the curves then won't that change the original equation of the curve?

Yes that would change the equations but then you would a problem that you can solve:

revolution techniques I know are rotating a curve about the x-axis and y-axis.

 

[ahsanxr]

Can that be applied to every problem?