MA 141 Study Guide - Final Guide: Riemann Sum, 4Dx, Classification Of Discontinuities
Document Summary
Now we will consider functions that may be above or below the x-axis. We will consider rectangles above the x-axis to have positive signed area and rectangles below the x-axis to have negative signed area. The riemann sum will then calculate the net area. Def: let f (x) be de ned and continuous on the interval [a, b]. For each partition a = x0 < x1 < x2 < . < xn 1 < xn = b of the interval [a, b] into n equal parts, the length of each and each xi = a + i x, i = 1, 2, . , n. the de nite integral of subinterval is x = f on [a, b] is denoted and de ned by. Z b a f (x)dx = lim n n. If the limit exists, we call f integrable on the interval [a, b]. Here, a and b are called the limits of integration.
