anonymous
  • anonymous
what is the integral of 1/2x+sinx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zepdrix
  • zepdrix
\(\large \int\dfrac{1}{2x}+\sin x\;dx\) Like this? Or is the sine suppose to be in the denominator?
anonymous
  • anonymous
it is \[\int\limits(1\div2)x + sinx\]
anonymous
  • anonymous
my computer is silly and doesn't do the fraction properly

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zepdrix
  • zepdrix
oh i see :)
zepdrix
  • zepdrix
\[\large \int\limits \frac{1}{2}x+\sin x\;dx\]We can integrate each term individually if that will help,\[\large =\int\limits \frac{1}{2}x\;dx+\int\limits\sin x\;dx\] For the x term we just need to apply the `Power Rule for Integration`. Remember how to do that? It involves two steps: ~Add 1 to the power. ~Then divide by the new power. \(\large \int x^n\;dx=\frac{1}{n+1}x^{n+1}\)
zepdrix
  • zepdrix
The 1/2 is a constant, let's pull that out of the integral so we don't have to worry about it. \[\large \frac{1}{2}\int\limits x^1\;dx\]Our x is x to the `first` power. Applying this rule gives us,\[\large \frac{1}{2}\left(\frac{1}{1+1}x^{1+1}\right)\qquad =\qquad \frac{1}{2}\left(\frac{1}{2}x^2\right)\]
zepdrix
  • zepdrix
Understand that part? :o
anonymous
  • anonymous
yep :) could you just make it 1/4 x^2?
zepdrix
  • zepdrix
Yes that sounds right. So here's where we're at currently, \[\large =\int\limits\limits \frac{1}{2}x\;dx+\int\limits\limits\sin x\;dx\] \[\large =\frac{1}{4}x^2+\int\limits\limits\sin x\;dx\]
zepdrix
  • zepdrix
Do you remember your trig derivatives? :O
anonymous
  • anonymous
-cosx
zepdrix
  • zepdrix
\[\large \frac{1}{4}x^2-\cos x+C\] Yay good job :D Psshh you didn't need help! Seems like you've got this pretty good. Just don't forget to add a constant of integration since it's an indefinite integral.
anonymous
  • anonymous
yep :) I just wasn't sure what to do because there were was more than 1 x in the equation
zepdrix
  • zepdrix
ah c:
anonymous
  • anonymous
thanks :P

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