# day11 - Math 1432 Section 12869 10 11 MWF Bekki George...

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Math 1432 Section 12869 10 – 11 MWF Bekki George [email protected] 639 PGH Office Hours in 639 PGH: MW 11am – 12:45pm Class webpage: http://www.math.uh.edu/~bekki/Math1432.html Test 2 will take place in the CASA Testing Center in less than 2 weeks. Starts Thursday, February 13 th . Schedule your time on Courseware. Practice Test 2 is a quiz grade and bonus (+5%).

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POPPER06 1. cos x sin 3 x dx
cos 2 x dx sin 2 x dx

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Recap: Sine and cosine with at least one odd power – Sine and cosine with both powers even –
Integrals involving Secants and Tangents tan 2 x + 1 = sec 2 x For tan m x sec n x dx a. n even: rewrite tan m x sec n x as tan m x sec n 2 x sec 2 x (then you can use identity 1 tan sec 2 2 + = x x ) b. m odd: rewrite as tan m 1 x sec n 1 x sec x tan x ( m -1 is even so can use identity tan 2 x = sec 2 x 1 ) c. m even and n odd: rewrite tan m x using tan 2 x = sec 2 x 1

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Examples: tan 3 ( x ) dx
4 sec xdx

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42 sec tan xx d x
sec x tan 2 x dx

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tan 3 x dx
sec 5 x tan x dx

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Integrals involving Sine-Cosine Products with Different Angles

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