MATH 181 Study Guide - Final Guide: 32X
Document Summary
Problem 1 solution: evaluate the integral ! cos3 x dx. Solution: the integral can be solved by rewriting it using the pythagorean identity cos2 x+ sin2 x = 1. cos3 x dx = ! cos2 x cos x dx. Then du = cos x dx and we get: cos3 x dx = ! Problem 2 solution: evaluate the integral ! xe3x dx. Solution: we will evaluate the integral using integration by parts. Let u = x and v = e3x. Using the integration by parts formula: uv dx = uv ! u v dx we get: xe3x dx = xe3x xe3x. Problem 3 solution: evaluate the de nite integral ! Solution: we evaluate the integral using the u-substitution method. Then du = 3x2 dx u = 1 + 23 = 9. The limits of integration becomes u = 1 + 03 = 1 and. The formula we will use to compute the area of the region is:
