Luigi0210
  • Luigi0210
solve the integral
Mathematics
schrodinger
  • schrodinger
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Luigi0210
  • Luigi0210
\[\int\limits_{0}^{4}(1-\sqrt{u})/(\sqrt{u})\]
anonymous
  • anonymous
Lolz...didn't even neded to substitute.
anonymous
  • anonymous
need*

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anonymous
  • anonymous
waste of your time.
zepdrix
  • zepdrix
Yah the substitution was kinda silly :) If you do a substitution, don't forget to change the limits of integration also.
anonymous
  • anonymous
And there's no du at the back of the integral
anonymous
  • anonymous
So there's no solution
anonymous
  • anonymous
You can't continue on integrating that without respect of anything.
Luigi0210
  • Luigi0210
Ops, sorry forgot about the du.. It is in respect to du
anonymous
  • anonymous
What are you integrating with respect to? You integrating with respect to zero?
anonymous
  • anonymous
Okay. Now you can integrate it. Just separate the numerator.
anonymous
  • anonymous
And you can continue integrating per usual.
anonymous
  • anonymous
\[\int\limits_{}^{}\frac{ 1 }{ \sqrt{u} }du-\int\limits_{}^{}1du\]\[\int\limits_{}^{}u^{-\frac{ 1 }{ 2 }}du-u\]\[2u^{\frac{ 1 }{ 2 }}-u\]Then just plug in the limit from 0 to 4
Luigi0210
  • Luigi0210
My only real problem is finding the anti-derivative
anonymous
  • anonymous
Anti-differentiating is just differentiating in reverse. Try and use reverse psychology when integrating if you can.
zepdrix
  • zepdrix
\[\large \frac{1-\sqrt u}{\sqrt u} \qquad = \qquad \frac{1}{\sqrt u}-\frac{\sqrt u}{\sqrt u} \qquad = \qquad u^{-1/2}-1\] Yah you just apply the `Power Rule for Integration`! :D
Luigi0210
  • Luigi0210
Thank you very much

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