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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 xdx Example 1.2. ± sin xdx = Example 1.3. ± sec 2 xdx = Example 1.4. ± sec x tan xdx = Example 1.5. (hint: change to sines and cosines and substitute) ± tan xdx = In integration by parts we learned some reduction formulas Theorem 1.1 (7.1 Example 6) . ± sin n xdx = - 1 n cos x sin n - 1 x + n - 1 n ± sin n - 2 xdx for n 2 Theorem 1.2 (7.1 Exercise 42) . ± cos n xdx = 1 n cos n - 1 x sin x + n - 1 n ± cos n - 2 xdx for n 2 Theorem 1.3 (7.1 Exercise 48) . ± sec n xdx = tan x sec n - 2 x n - 1 + n - 2 n - 1 ± sec n - 2 xdx 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
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sec7_2 - 7.2 Trigonometric Integrals 1. Review Recall from...

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