1. The problem statement, all variables and given/known data The curve y=1/x and the line y=2.5-x enclose an area together. Determine the exact volume of the rotating body that is formed when this field rotates about a) The x-axis and b) The y-axis 2. Relevant equations The formula for rotation around the x-axis is pi*integrate from b to a y^2 dy.. The formula for rotation around the y-axis is pi*integrate from d to c x^2 dx. 3. The attempt at a solution I'm gonna start with a). So what I've learned is that around the x-axis, first I have to find the points from where I'm gonna integrate (i.e. integrate from z to y and so on). To get these two points, I'm going to put the curve equal to the line so I know where they intersect. 2.5-x=1/x => 2.5x-x^2=1 => x^2-2.5x+1 = 0 and I get x(1) = 2 and x(2) = 0.5. So if I'm going to find out the answer, I'll also use (1/x)^2 - (2.5-x)^2. So the total would be: pi * integrate from 2 to 0.5 for (1/x)^2 - (2.5-x)^2 which gives me the correct answer 1.125*pi. Okay, so how do I do it for b then? Take a look here: http://www.wolframalpha.com/input/?i=y=1/x,+y=2.5-x I want to calculate the volume for the rotation that is both under the purple and blue line. But how do I get that? It is obvious that the "integration limits" are from 2.5 to 0 from that graph. But how do I express it in a formula? If I do the same as earlier, (1/x) - (2.5-x) Then doesn't that area under the purple line eliminate all of it that is under the blue and then some?