## Luigi0210 2 years ago solve the integral

1. Luigi0210

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

2. Azteck

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

3. Azteck

need*

4. Azteck

5. zepdrix

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

6. Azteck

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

7. Azteck

So there's no solution

8. Azteck

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. Azteck

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

11. Azteck

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

12. Azteck

And you can continue integrating per usual.

13. Lynncake

$\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. Azteck

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