# Thread: I don't know what I did wrong on this integral..

1. ## I don't know what I did wrong on this integral..

Question is: Evaluate $\displaystyle \int_{25}^{36}\frac{ln(y)}{\sqrt(y)}dy$

Integrating by parts,
$\displaystyle u=ln(y), du=\frac{dy}{y}$
$\displaystyle dv=\frac{1}{\sqrt{y}}dy, v = 2\sqrt{y}$

$\displaystyle =[2\sqrt{y}ln(y) - 2\int\frac{1}{\sqrt{y}}dy]_{25}^{36}$

$\displaystyle = [2\sqrt{y}ln(y) - 4\sqrt{y}]_{25}^{36}$

$\displaystyle =(12ln(36)-24) - (10log25-20)$

$\displaystyle =12log36-10log25-4$

Strangely this is the same answer that Wolfram Alpha gives, but the decimal value is different. When evaluated on my calculator I'm getting 0.696, the correct answer is 6.813 can someone point out my error? Thanks!

2. You changed the "ln" to a "log".
$\displaystyle ln=log_{e}$
$\displaystyle log=log_{10}$
Big difference.

3. you are using log when you should be using ln (natural log) yes the base matters.... =) no mistakes with calculus, just logarithms

4. That's the second time in a row I made that same mistake! Maybe it's my lack of sleep...haha thank you guys!