Finding the Volume of a Solid by Revolving a Region

[science.girl]

Problem:
Find the volume of a solid generated by revolving the region bounded by the graphs of y = x^2 - 4x +5 and y = 5- x about the line y = -1.

Attempt:
Do I find where the graphs intersect, then make those values the upper and lower bounds for the integral?

And could I set the problem up by having the integral of: [((5 - x) -1) - ((x^2 - 4x +5) - 1)]dx



Thanks! (And my apologies -- I'm having issues with the template.)

 

[HallsofIvy]

Problem:
Find the volume of a solid generated by revolving the region bounded by the graphs of y = x^2 - 4x +5 and y = 5- x about the line y = -1.

Attempt:
Do I find where the graphs intersect, then make those values the upper and lower bounds for the integral?

And could I set the problem up by having the integral of: [((5 - x) -1) - ((x^2 - 4x +5) - 1)]dx



Thanks! (And my apologies -- I'm having issues with the template.)

Yes, you need to find the points where they intersect. But that integral looks like the integral for the area between the the two curves, not the volume of the rotated region. Imagine a thin slice between, say, x and dx, rotated around the line y= -1. What figure does that look like? What is its volume?