Section7.3-Trigonometric+Substitution

3cos 3cos d 2 x sin 2 whatis 2 a 3 x 3sin

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Unformatted text preview: e substitution: dx x x 5sec dx 5 tan sec d x θ 1 25sec 25 2 5 tan sec d 5 tan sec 25 sec 2 1 A) x 3sin , d x 5 tan ln sec tan C ln 5 tan sec d 5 tan dx 9 tan sec d D) x 3sec , x x 2 25 C 5 5 dx 3sec 2 d C) x 9sec , x 2 25 5 dx 3cos d B) x 3 tan , 5 sec x 9 x 2 25 dx 3 tan sec d ln x x 2 25 ln 5 C sec d ln x x 2 25 C ln sec tan C Quiz Quiz Using the substitution, , x 3sec , dx 3 tan sec d x dx x 9 2 2 9sec A) x 1 1 cos d sin C 2 9 9 x 9 2 d x2 9 C x A) 1 9 cos d 11 C 3x C) 2 1 9 B) tan d B) 27 sec 2 tan C) dx 1 9 x x 9 2 Example 1 0 Example ‐ continued x 3 x 2 4dx 32 tan x 2 tan First, find antiderivative: x 3 32 tan x 2 4dx 8 tan 8 tan 3 3 4 tan 2 4 2sec2 d 4 tan 1 2sec d 2 2 2 8 tan 2 sec 2sec d 3 3 x sec3 d u sec du sec tan d dx 2sec 2 d C x 2 4dx 32 u 4 u 2 du 3 x x tan u sec 2 _________________ 0 sec tan sec d 2 32 u 4 1 2 4 1 1 5 5 5 5 32 3 3 5 1 2 2 2 32 sec 1 sec tan sec d 32 u 0 1 2 3 55 5 11 32 5 3 2 5 2 3 5 3 1 u 2 du u 2 du 1 0 5 2 5 x3 x 2 4dx 2 32 u 4 u 2 du 1 64 5 5 15 3 64 25 5 15 5 u5 u3 2 32 5 3 1 1 0 x3 x 2 4dx 64 25 5 15 2 9/3/2013 Try 1 9 x 2 dx Try 2 1 dx x2 x2 4 3...
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

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