# Thread: Finding A Definete Integral (Without Int. by Parts)

1. ## Finding A Definete Integral (Without Int. by Parts)

I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx

Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong.

2. You don't need parts or any other techniques, just plain ol' strightforward integration.

$\frac{1+\sqrt{x}}{\sqrt{x}}=x^{\frac{-1}{2}}+1$

$\int_{4}^{9}\left[x^{\frac{-1}{2}}+1\right]dx=7$

3. Originally Posted by SportfreundeKeaneKent
I need to find the definite integral between 4 and 9 where the function is [1+sqrt(x)]/sqrt(x) dx

Without using integration by parts. I got 35*1/3 but I'm sure the way I did this was wrong.
Or if you meant something like

$\int_a^{b}\frac{(1+\sqrt{x})^n}{\sqrt{x}}dx=2\int_ a^b\frac{(1+\sqrt{x})^n}{2\sqrt{x}}dx=\frac{2(1+\s qrt{x})^{n+1}}{n+1}\bigg|_{a}^b$