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Question
Find the integrals of the function:
sin 3x cos 4x
Solution
Let `I = int sin 3x cos 4 x dx`
`1/2 int [sin (3x + 4x) + sin (3x - 4x)] dx` ...[∵ 2 sin A cos B = sin (A + B) + sin (A - B)]
`= 1/2 int [sin 7 x + sin (-x)] dx`
`= 1/2 int (sin 7x - sin x) dx`
`= 1/2 ((-cos 7x)/7) - 1/2 (-cos x) + C`
`= -1/14 cos 7x + 1/2 cos x + C`
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