MATH 181 Study Guide - Final Guide: Scilab, Ratio Test, Absolute Convergence

• School: UIC
• Department: Mathematics
• Course: MATH 181
• Professor: All

Document Summary

Solution: (a) z x cos(3x) dx (b) z sin x. 3 cos x dx (a) we will evaluate the integral using integration by parts. Let u = x and v = cos(3x). sin(3x). Z uv dx = uv z u v dx. Then u = 1 and v = we get: 3 x sin(3x) z 1 x sin(3x) (cid:20) . 9 cos(3x) + c (b) we will evaluate the integral using the u-substitution method. Then du = sin x dx and we get: 1 x2 ln x dx (a) we will evaluate the integral using partial fraction decomposition. First, we factor the denominator and then decompose the rational function into a sum of simpler rational functions. Next, we multiply the above equation by (2 x)(2 + x) to get: 1 = a(2 + x) + b(2 x) Then we plug in two di erent values for x to create a system of two equations in two unknowns (a, b).