# Integration problem 1

1. Feb 20, 2013

### PhizKid

1. The problem statement, all variables and given/known data
$\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx$

2. Relevant equations

3. The attempt at a solution
$\int_{4}^{9} (\sqrt{x} + \frac{1}{\sqrt{x}})^{2} \textrm{ } dx \\\\ \int_{4}^{9} (x + 1 + 1 + \frac{1}{x}) \textrm{ } dx \\\\ \frac{x^2}{2} + 2x + ln(x) | \textrm{4 to 9} \\\\ (27 + ln(9)) - (\frac{88}{9} + ln(4)) \\\\ \frac{155}{9} + ln(\frac{9}{4})$

The solution says this is incorrect...can anyone correct me where I integrated wrong?

2. Feb 20, 2013

### bossman27

I think you just goofed up when plugging in 9 and 4. Everything up until that point is correct.

3. Feb 20, 2013

### Staff: Mentor

Your integration was fine. You have a mistake when you evaluate your antiderivative, when x = 4. If x = 4, x2/2 = 16/2, not 88/9.

4. Feb 20, 2013

### Zondrina

$9^2 ≠ 27$

In specific : x^2/2 = 81/2

Last edited: Feb 20, 2013