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hw2 - 2 cos n xdx(i Prove that I n = n-1 n I n-2(ii Using...

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 2. Due January 22. 2.1. First use a substitution, then integration by parts to evaluate Z sin(ln x ) dx. 2.2. Evaluate Z π 0 e cos t sin 2 t dt. 2.3. Use integration by parts to prove the reduction formula Z sec n x dx = tan x sec n - 2 x n - 1 + n - 2 n - 1 Z sec n - 2 x dx. 2.4. Evaluate Z sin x cos 3 x dx. 2.5. Evaluate Z dx sin x - 1 . 2.6. Let
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Unformatted text preview: 2 cos n xdx. (i) Prove that I n = n-1 n I n-2 . (ii) Using the reduction formula from part (i), evaluate R π/ 2 cos 8 xdx . 2.7. Evaluate Z (cos-1 x ) 2 dx. Here cos-1 x = arccos x is the inverse function to cos x . ( Hint: Use integration by parts twice.) 1...
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