Imagine we would like to determine the volume of solid S. We start by placing it over the xy-plane with end points given by x = a and x = b. For each x in the interval [a, b] we define A(x) to be the area of the perpendicular cross-section to Sat x. y 0 A(a) a S A(x) P A(b) b Vol(S) = f*A(x) dx a b x It turns out that volume of S is given by the following simple definite integral: In this project we'll explore how this formula can be used in conjunction with modern medical imagining techniques to determine the volume of internal organs. If we were to perform many more CT scans we could build up a more complete understanding of the cross-sectional area function. In principle, we could approximate this function by one we can integrate, thus giving a more sophisticated approximation to the volume. Imagine now that we have performed enough CT scans to determine that A(x) is approximated by the function x5 ex on the interval [0, 2]. Using this, approximate the volume. Solution: f(x) =