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Integrals, Substitution, and Partial Fractions

by: Guadalupe Alvarez

Integrals, Substitution, and Partial Fractions MTH 162

Marketplace > University of Miami > Math > MTH 162 > Integrals Substitution and Partial Fractions
Guadalupe Alvarez
GPA 3.45
Calculus 2

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Here is the study guide for trigonometric integrals, substitution and partial fractions. Let's Ace that Midterm!
Calculus 2
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This 2 page Study Guide was uploaded by Guadalupe Alvarez on Friday February 13, 2015. The Study Guide belongs to MTH 162 at University of Miami taught by Draghici in Spring2015. Since its upload, it has received 86 views. For similar materials see Calculus 2 in Math at University of Miami.


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Date Created: 02/13/15
MTH 162 Trigonometric Integrals Trigonometric Substitution and Partial Fractions 1 Evaluate the integral 3 5 a sin2acos3ada 8m x 8m x C 3 5 7T2 7 5 1 b 39 6 6 f0 s1n cos 120 C cos42t dt 2 E71 0 8 27 1 3 d sin2 6 d3 71 I 0 3 8 1 1 1 cos2 1 d3 12 E sin21 g cos23 C 6 tan233da tan33 33 l C 4 4 2 f 00s2atan3ada 1ncos1 CO 3 C 3 sec3a g tanazsec da 3 C t 5 t 7 t 9 h tan4xsec6ada a1 xl a1 xl a1 xlC 1 2 Evaluate the following integrals 1 2 a 33x1 332d332 0 15 2 1 3 1 dt1 5731752 1 24 8 4 2 4 C 33x332 4da 1 0 d d3 1 0 a2232 a2 V332 16 1 4 4 Cln12 16 13 C 1n e d3 V332 16 1 f 1 4132 d3 Z sin 1233 231 4132 C E V5 u2 U U 1 du guv5 u2z 0 1n 2 h 39dS C1 332 9C 06 2 97 i dx l 0 x9 2532 500 Evaluate the following integrals 4 4 3 2 a fxildxzxz I xg I xE I x l lnlx ll l C 51 1 1 b d 1 2 1 21 1 C 233113 1x 2Ill 33 3933 H 1 4 2 4 2 12 2 y 7y dy 7an 2ln3 2ln 1 yy2y 3 5 5 5 3 332 53316 3 d l 2 1 e 21 133 22 75 21139 I 3333322331 1 1 1 1 2 1 1 2122d 211w tan c 1 1 1 1 2 1 g f dajz glnx 1 6l11132 33 1 tan 1 0 ln1 2 C 513 2 3 1 x3 2x2 l 33 I 1 1 3 a 1 2 4 1 1 h x4524 d3 2n1 2tan 2 tan x I C 3341 1 39 d 1 IWm n2x m e1c Make a substitution to express the integrand as a rational function and then evaluate the integral 16 2 a d12 ln35 9 513 4 6230 em 22 blfg rg n x m7zrr0


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