MATH 182A Lecture Notes - Lecture 6: Riemann Sum
Document Summary
Normally we would solve this problem by integrating r ex2. = f (x) and then using the fundamental theorem of calculus (f (1) f (0)). However, there is no known way to integrate ex2 (or at least it becomes very di cult). We can nd a numerical approximation of it instead. Z b a n f (x)dx = lim f (x i ) x. When we integrate, we are taking the sum of areas of rectangles under the curve as the width of the rectangle approaches 0. this gives us an exact value. If we cannot do that, then we can approximate the integral by removing the limit. n. Z b a f (x)dx f (x i ) x. This splits the integral into n discrete points, each of which we can calculate a rectangular area from. = x(cid:20)f (x0) + f (x1) + + f (xn 1)(cid:21)
