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8.3 Trigonometric Integrals

8.3 Trigonometric Integrals. Math 6B Calculus II. Strategies for Evaluating . If m is odd and n is real Split off sin x , rewrite the resulting even power of sin x in terms of cos x, and then use u = cos x. If n is odd and n is real

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8.3 Trigonometric Integrals

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  1. 8.3 Trigonometric Integrals Math 6B Calculus II

  2. Strategies for Evaluating • If m is odd and n is real Split off sin x, rewrite the resulting even power of sin x in terms of cosx, and then use u = cosx. • If n is odd and n is real Split off cosx, rewrite the resulting even power of cosx in terms of sin x, and then use u = sin x.

  3. Strategies for Evaluating • If m and n are both even, nonnegative integers Use half – angle identities to transform the integrand into a polynomial of cos 2x and apply the preceding strategies once again to power of cos 2x greater than 1.

  4. Strategies for Evaluating • If m is odd Split off sec x tan x, rewrite the remaining even power of tan x in terms of sec x and use u = sec x. • If n is even Split off , rewrite the remaining even power of sec x in terms of tan x, and use u = tan x.

  5. Strategies for Evaluating • If m is even and n is odd We would use a reduction formula (we will not be covering this)

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