pogan1AK - Answer Key for Prof. Pogan's Sample Math 1272...

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Answer Key for Prof. Pogan’s Sample Math 1272 Mid-term I 1) a) e x dx = 2 5 e 5 x ( x 1) + C [use a rationalizing substitution] b) dx x 2 x 2 + 25 = 1 25 x 2 + 25 x + C [use a trigonometric substitution] c) sin 7 x cos 4 x dx = 7 33 0 π / 2 [use the product-to-sum trigonometric formulae] d) e x e 2 x + 4 e x + 20 0 ln 3 dx = 1 4 tan 1 ( 5 4 ) tan 1 ( 3 4 ) [ ] [make a substitution for e x , then complete the square in the denominator] 2) A x + B x 2 + C x 3 + D x 4 + Ex + F x 2 + 3 + Gx + H ( x 2 + 3) 2 3) write (tan x sec x ) 8 dx = tan 8 x sec 6 x sec 2 x dx , make the substitution u = tan x , du = sec 2 x dx , then use the Pythagorean
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This note was uploaded on 10/05/2011 for the course MATH 1272 taught by Professor Wilson during the Spring '08 term at Minnesota.

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