Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution Va - z = a sin 0, – sos a tan 0, - < 0 < a sec 8, 0<0< 풀or 플 <8<ㅠ Va? + a² V – a? Part 1. Using the substitution: æ = 2 sec 0 , 0 < 0 < , re-write the indefinite integral then evaluate in terms of 0. Suppose that z > 2. Then, dr Note: type 'theta' for 0 and 'dtheta' for de. Part 2. Back substituting in the antiderivative you found in Part 1. above we have dæ =O dz

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter6: Trigonometric Functions: Unit Circle Approach
Section6.2: Trigonometric Functions Of Real Numbers
Problem 79E
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Trigonometric Substitutions
The three basic trigonometric substitutions are in the table below.
Integral Contains Try using Substitution
Va? – 22
Va? + z?
z = a sin 0, - 0<
-플 <8<
a sec 8, 0<8< 들 or플 <8<ㅠ
a tan 0,
Part 1.
Using the substitution: a =
2 sec e ,0 <0 <, re-write the indefinite integral then evaluate in terms of 0.
Suppose that z > 2. Then,
dr =
Note: type 'theta' for 0 and 'dtheta' for de.
Part 2.
Back substituting in the antiderivative you found in Part 1. above wve have
dz
Note: answer should be in terms of z only.
Transcribed Image Text:Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution Va? – 22 Va? + z? z = a sin 0, - 0< -플 <8< a sec 8, 0<8< 들 or플 <8<ㅠ a tan 0, Part 1. Using the substitution: a = 2 sec e ,0 <0 <, re-write the indefinite integral then evaluate in terms of 0. Suppose that z > 2. Then, dr = Note: type 'theta' for 0 and 'dtheta' for de. Part 2. Back substituting in the antiderivative you found in Part 1. above wve have dz Note: answer should be in terms of z only.
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