Find the height of the frustum. The height of the frustum is the distance between the two lines cutting the cone. Call this height "h."
Find the radii of the two circles composing the top and bottom of the frustum. Measure from the center of the bottom circle out to the edge of the bottom circle. Call this distance "ra." Do the same for the top circle, and call that distance "rb."
Set up the integral that computes the frustum. Write "pi*int(ra-(z/h)ra+rb)^2dz." Here, "pi" is the number pi, 3.14159..., "int" stands for the integral and "z" is the variable you are integrating over, as evident by "dz."
Set the bounds on the integral. The lower bound is 0, and the upper bound is "h."
Solve the integral. Use standard calculus to reduce the integral to a sum of variables. The solution is pi*h*(ra^2+ra*rb+rb^2)/3.
Evaluate the integral using the limits. Because the lower limit is zero, you only need to plug "h," "ra" and "rb" into the solution for the integral. For example, if your frustum has a height of 2, a lower-circle radius of 2 and a upper-circle radius of 1, the solution for the frustum will be pi*2*(2^2+2+1^2) or 14pi.