Find the square of the profile function that traces out the solid of revolution. The general method for finding the volume of a solid of revolution is integrating pi * (f(x))^2. Pi is a constant, so move it outside of the integral and square the profile function. For example, given the function f(x) = x^2/9 + 1, (f(x))^2 = x^4/81 + 2x^2/9 + 1.
Find the anti-derivative of the squared function. For example, g(x) = the anti-derivative of (f(x))^2 = x^5/405 + 2x^3/27 + x + K, where K is some constant. The value of K is unimportant, since it gets eliminated in the next step.
Evaluate the integral within the defined bounds. For example, given the bounds [0, 3], find the difference g(3) - g(0). Plug those values into the function, g(3) = 3/5 + 2 + 3 + K = 28/5 + K, and g(0) = K. Therefore, g(3) - g(0) = 28/5.
Find the volume by multiplying the evaluated integral by pi. The volume of the solid given in the example would be 28 * pi/5, which is 17.6.