MATH 2B Chapter Notes - Chapter 6.1: Riemann Sum

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

Computing the area between two curves is no harder than. Area = z b a f (x) dx z b a g(x) dx = z b a f (x) g(x) dx. More generally we can nd the area between curves f (x) g(x) by taking limits of a riemann sum: note that the heights of the approximating rectangles are the difference between the values of f and g. a. Area = lim n n i=1 ( f (x i ) g(x i )) x = z b a f (x) g(x) dx. Examples: find the area between y = x and y = 2 x2 for 1 x 1. 2 x2 x dx = 2z 1. 2 x x2 = x2 3x 2. = 0 = 2x2 2x 4 = 2(x 2)(x + 1) 2 x x2 (x2 3x 2) dx = z 2. = 12 + 3 6 = 9 x3(cid:12)(cid:12)(cid:12)