# MA122 Study Guide - Final Guide: Trapezoidal Rule, Riemann Sum, Differentiable Function

## Document Summary

Things to memorize is continuous on [a, b] and. Leibniz theorem differentia(cid:271)le on (cid:894)a, (cid:271)(cid:895), and g"(cid:894)(cid:454)(cid:895) = f(cid:894)(cid:454)(cid:895) Part 2: if f is continuous on [a, b], then (cid:4666) (cid:4667) (cid:4666) (cid:4667) Part 1: if f is continuous on [a, b], then (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4666) (cid:4667)(cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) ( (cid:4666) (cid:4667)) ( (cid:4666) (cid:4667)) (cid:4666) (cid:4667) ( (cid:4666) (cid:4667)) (cid:4666) (cid:4667) (cid:4666) (cid:4667) If u = g(x) is a differentiable function whose range is an interval i, and f is continuous on i, then. If f is even, f(-x) = f(x) and so (cid:4666) (cid:4667) (cid:4666) (cid:4667) If f is odd, f(-x) = - f(x) and so (cid:4666) (cid:4667) (cid:4666) (cid:4667) (cid:4666) (cid:4667) u = sinx and du = cosx dx. When n = 2k + 1 = odd (cid:4666) (cid:4667)