MATH 181 Study Guide - Final Guide: Absolute Convergence, Improper Integral, Ibm System P
Document Summary
Problem 1 solution: compute the inde nite integral: We now evaluate the integral using the u-substitution method. = z dx (x + 2)2 + 1 du u2 + 1. Problem 2 solution: determine if the following improper integrals converge or not. 1 x + 1 x2 + x + 1 dx. Solution: each integral is improper due to the in nite upper limit of integration. We evaluate the rst integral by turning it into a limit calculation. We use integration by parts to compute the integral. Let u = x and v = e x. Using the integration by parts formula we get: Z r xe x dx = h xe xir. We now take the limit of the above function as r + . xe x dx xe x dx = lim. R er 0 + 1 (r) (er) 0 + 1. We will show that the second integral diverges using the comparison test.
