anonymous
  • anonymous
How do I solve "integral [ sin(x) * cos(x) ] dx" ?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\int\limits_{?}^{?} [ \sin(x) * \cos(x) ] dx\]
anonymous
  • anonymous
Try u-substitution. Let u = sin(x). This means that du=cos(x)dx. Now it's ready to substitute back in the original equation to get: \[\int\limits_{?}^{?}udu\] This integral is (1/2)u^2 + c. Substituting back in for x you get: (1/2)sin^2(x) + c
anonymous
  • anonymous
is it possible to do it with partial integration?

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anonymous
  • anonymous
also ... how do i know i have to do substitution? i mean ... i can easily get the antiderivative of both sin(x) and cos(x) ..
anonymous
  • anonymous
but getting an antiderivative of cos(x)sin(x) is different. You might be able to get it using parts but it would be more work than it's worth. When ever I do integrals I always ask myself first if I know an antiderivative and if I don't I move to u-sub because I find u-sub to be the next easiest.

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