## Luigi0210 3 years ago solve the integral

1. Luigi0210

$\int\limits_{0}^{4}(1-\sqrt{u})/(\sqrt{u})$

2. anonymous

Lolz...didn't even neded to substitute.

3. anonymous

need*

4. anonymous

5. zepdrix

Yah the substitution was kinda silly :) If you do a substitution, don't forget to change the limits of integration also.

6. anonymous

And there's no du at the back of the integral

7. anonymous

So there's no solution

8. anonymous

You can't continue on integrating that without respect of anything.

9. Luigi0210

Ops, sorry forgot about the du.. It is in respect to du

10. anonymous

What are you integrating with respect to? You integrating with respect to zero?

11. anonymous

Okay. Now you can integrate it. Just separate the numerator.

12. anonymous

And you can continue integrating per usual.

13. 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

14. Luigi0210

My only real problem is finding the anti-derivative

15. anonymous

Anti-differentiating is just differentiating in reverse. Try and use reverse psychology when integrating if you can.

16. 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

17. Luigi0210

Thank you very much