MATH 2B Study Guide - Midterm Guide: Inverse Trigonometric Functions, Scilab, Partial Fraction Decomposition

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: All

Document Summary

Math 2b, winter 2015, lecture j: midterm 2. A correct answer by itself may earn no points if you do not clearly indicate the steps of your solution: academic dishonesty in any form will result in a score of zero, evaluate the following inde nite integrals. [12 points each] (a) (b) (cid:90) x sec2 x dx = x tan x x sec2 x dx (cid:90) Since the integrand is a product of a power of x with a trig functions, it"s a good idea (cid:90) to try integration by parts: (cid:82) u dv = uv (cid:82) v du. If we take u = x, we"re left with dv = sec2 x dx, so du = dx and we can take v =(cid:82) sec2 x dx = tan x. X < 3 (cid:90) (cid:90) (cid:90) cos d . + c, dx x2 4 suggests the substitution x = 2 sec , with 0 < .