L15a - Trigonometric Substitutions

L15a - Trigonometric Substitutions - Trigonometric...

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Trigonometric Substitution (part 1) (Section 7.3) Review: Ex. Suppose we used x 3sec to make a substitution and ended with the following integral:  sin 2 tan C Convert the expression back to an expression in x. Ex. Suppose we used x 5 tan to make the substitution and ended with the integral: cos  3sin      C Convert the expression back to an expression in x.
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Now, suppose we have an integral of the form a 2 x 2 dx . We cannot use u substitution. Why? Instead we will substitute x a sin with dx a cos d . a 2 x 2 dx = RULES FOR TRIG SUBSTITUTION (trig change of variables) If An Integrand Contains: Use: 1.  22 2 , 0 n ax n  x a sin Since sin 2  cos
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L15a - Trigonometric Substitutions - Trigonometric...

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