Question

integration of sin x square dx​

Answer 1

Answer:

This is a problem of trigonometry, rather than integration.

sin^2(x) = 1- cos^2(x) = 1- (cos(2x) +1) /2 = 0.5 - cos(2x)/2.

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Since, cos^2(x) = (cos(2x) +1) /2. This is cosine double angle formula.

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Now, integration of 0.5 is 0.5x = x/2.

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Integration of cos(2x) is sin(2x)/2.

Integration of cos(2x)/2 is sin(2x)/4.

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Hence the integration of sin^2(x) w.r.t. x is x/2 - sin(2x)/4 + C.