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