What is the antiderivative of f(x)=sinxcosx?

4 Answers

  • f(x) = (1/2)sin2x

    So, the antiderivative of f(x) = -(1/4)cos2x + c

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  • Anti derivative of sinx cox can be calculated as follows:

    Use logarithmic equation: sin(2x) = 2 sinx cosx, therefore, sin(2x) / 2 = sinx cos x

    ∫sinx cosx dx = ∫ sin(2x)/2 dx = (1/2) ∫ sin(2x) dx = (1/2) (-1/2) cos(2x) + C

    Solution: (-1/4)cos(2x) + C

  • Let u = sin x, then du = cos x dx.

    Substitute you have integral u du = u^2/2 + C.

    Subing back gets you: (sin^2 x)/2 + C

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