Evaluate 7 sin (x) cos (x) dx by four methods. (a) the substitution u = cos (x) 7 4 cos (2x) + c - 7 2 sin2 (x) + c 7 4 sin (2x) + c 7 4 sin (x) cos (x) + c - 7 2 cos2 (x) + c (b) the substitution u = sin (x) 7 2 sin2 (x) + c 7 4 cos (2x) + c - 7 4 sin (2x) + c 7 4 sin (x) cos (x) + c 7 2 cos2 (x) + c (c) the identity sin (2x) = 2 sin (x) cos (x) - 7 2 sin2 (x) + c 7 4 sin (2x) + c - 7 4 sin (x) cos (x) + c 7 2 cos2 (x) + c - 7 4 cos (2x) + c (d) integration by parts 7 2 cos2 (x) + c - 7 4 sin (2x) + c 7 4 cos (2x) + c - 7 4 sin (x) cos (x) + c 7 2 sin2 (x) + c

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Marina Thompson

1 October, 13:19

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Gillian Duncan · Answer 1

(d) integration by parts 7 2 cos2 (x) + c - 7 4 sin (2x) + c 7 4 cos (2x) + c - 7 4 sin (x) cos (x) + c 7 2 sin2 (x) + c