MATH 1B Study Guide - Final Guide: Trigonometric Substitution, Telephone Numbers In The United Kingdom, Direct Comparison Test
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The exam is closed book, apart from a sheet of notes 8 x11 . It is your responsibility to write your answers clearly: (6 points) use substitution and integration by parts to nd: Solution: substituting s = tan x, ds = (sec x)2dx we have. Tan x(sec x)2 etan xdx = sesds. Now we use integration by parts: u = s, du = ds, dv = esds, v = es. Sesds = ses esds = ses es + c. Tan x(sec x)2 etan xdx = tan x etan x etan x + c: (6 points) use trigonometric substitution to evaluate. 1 sin2 d = csc2 d = cot + c. for t (0, 1). Solution: substitute t = sin , 0 < < . Cos2 = | cos | = cos since 0 < < . Then dt = cos d sin2 cos . We now go back to the original variable cot = cos sin =
