sec7_2 - 7.2 Trigonometric Integrals 1 Review Recall from...

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7.2 Trigonometric Integrals 1. Review Recall from Calculus I Example 1.1. cos x dx Example 1.2. sin x dx = Example 1.3. sec 2 x dx = Example 1.4. sec x tan x dx = Example 1.5. (hint: change to sines and cosines and substitute) tan x dx = In integration by parts we learned some reduction formulas Theorem 1.1 (7.1 Example 6) . sin n x dx = - 1 n cos x sin n - 1 x + n - 1 n sin n - 2 x dx for n 2 Theorem 1.2 (7.1 Exercise 42) . cos n x dx = 1 n cos n - 1 x sin x + n - 1 n cos n - 2 x dx for n 2 Theorem 1.3 (7.1 Exercise 48) . sec n x dx = tan x sec n - 2 x n - 1 + n - 2 n - 1 sec n - 2 x dx when n 2 Remark 1.1. You do not need to memorize reduction formulas , but should be able to use them. If I expect you to use any on an exam you will be given the formula. Or you may be expected to use one of the following alternative methods rather than an above formula 1
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Section 7.2 2 2. More Trigonometric Integrals – odd positive powers of Sine and Cosine Method: Save one factor of the function, use the identity sin 2 x + cos 2 x = 1 to get everything in terms of the cofunction, and substitute for the cofunction.
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