Lecture 4 (Trig Substitution)

Lecture 4 (Trig Substitution) - Tuesday, January 10 Lecture...

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Tuesday, January 10 Lecture 4 : More Integration Methods : Trigonometric Substitution ( Refers to Section 6.4 in your text ) After having practiced the problems associated to the concepts of this lecture the student should be able to : Solve integrals of functions containing a 2 x 2 , a 2 + x 2 or x 2 a 2 by applying an appropriate trig substitution, solve definite integrals by trig substitution. 4.1 The method called “Trigonometric substitution” This method applies to integrands containing a 2 x 2 , a 2 + x 2 or x 2 a 2 . It is summarized in the following table: Note The restriction x = a sec θ, 0 ≤ θ < π /2, π ≤ θ < 3 π /2 is due to the way θ = arcsec y is defined. That is, θ = arcsec y if and only if sec θ = y and θ ∈ [0, π /2) [ π , 3 π /2). The definition is not universal. But the important point is that inverse of trigonometric functions are defined on intervals where the function is one-to-one

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This note was uploaded on 04/01/2012 for the course MATH 118 taught by Professor Zhou during the Winter '08 term at Waterloo.

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Lecture 4 (Trig Substitution) - Tuesday, January 10 Lecture...

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