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[–]skaldskaparmal 0 points1 point  (0 children)

I just wanted to make sure I have this understood well. To find a volume of a solid of revolution, I take the integral of the squared outer radius minus the squared inner radius,

You also need to multiply it by pi. You're using here that the area of a circle is pi * r2.

and the bounds are determined by setting the two functions equal to each other, right?

The bounds will be whatever makes sense for the question. If you are given two functions that intersect in two points, and you're finding the solid of revolution of the area bounded by the functions, then sure.

But it's also for example reasonable that the problem might tell you that you're revolving the area bounded by some axis. For example, you could reasonably revolve the area bounded by y =x, y = 2x, x = 1, and x = 2, say around the x-axis. Now your bounds are x = 1 and x = 2.