anonymous
  • anonymous
how do i integrate cos^2x ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
standard trick is to rewrite using one of those trig reduction formulas that you thought you would never use
anonymous
  • anonymous
\[\cos^2(x)=\frac{1}{2}(\cos(2x)+1)\] integrate term by term
anonymous
  • anonymous
would the answer be 1/20 [1/2 sin 2x ] ?

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anonymous
  • anonymous
no i don't think so
anonymous
  • anonymous
\[\int 1dx=x\] \[\int \cos(2x)dx=-\frac{1}{2}\sin(2x)\]
anonymous
  • anonymous
sorry last one is wrong should be \[\int \cos(2x)dx=\frac{1}{2}\sin(2x)\]
anonymous
  • anonymous
ohh, i took out the one outside.
anonymous
  • anonymous
should get as a final answer \[\frac{x}{2}+\frac{1}{2}\sin(2x)\]
anonymous
  • anonymous
i gt 1/40 sin 2x + 1/20x
anonymous
  • anonymous
or if you like you can rewrite as \[\frac{x}{2}+\frac{1}{2}\sin(x)\cos(x)\] by that double angle formula. either way
anonymous
  • anonymous
damn another mistake, hold on
anonymous
  • anonymous
\[\frac{x}{2}+\frac{1}{4}\sin(2x)\] is correct
anonymous
  • anonymous
i assume the zeros in your answer are typos.
anonymous
  • anonymous
so the answer would be pi/2?
anonymous
  • anonymous
the answer is a function, or rather a class of funcitons, not a number
anonymous
  • anonymous
sorry i have to substitute pi and 0, as the last part.
anonymous
  • anonymous
thanks a lot for your help !

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