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Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution a- a sin 0, -

Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution a- a sin 0, -

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Trigonometric Substitutions The three basic trigonometric substitutions are in the table below. Integral Contains Try using Substitution Va – Va? + x? ? – a² x = a sin 0, - <0< I = a tan 0, z = asec 8, 0<θ< 폴 or 플 <8<ㅠ Part 1. Using the substitution: z = tan 0, -<0<, re-write the indefinite integral then evaluate in terms of 0. dx = Note: type 'theta' for 0 and 'dtheta' for de. Part 2. Back substituting in the antiderivative you found in Part 1. above we 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 – Va? + x? ? – a² x = a sin 0, - <0< I = a tan 0, z = asec 8, 0<θ< 폴 or 플 <8<ㅠ Part 1. Using the substitution: z = tan 0, -<0<, re-write the indefinite integral then evaluate in terms of 0. dx = Note: type 'theta' for 0 and 'dtheta' for de. Part 2. Back substituting in the antiderivative you found in Part 1. above we have dz Note: answer should be in terms of z only.
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