# definite integral integration

• Nov 17th 2008, 09:02 AM
2clients
definite integral integration
0
S x/sqrt(x+1) dx
-1
Any help would be greatly appreciated.

I tried setting:

u = x
du = dx
dv = 1/sqroot(x+1)
v = 2sqroot(x+1)

But everything is going to zero..
• Nov 17th 2008, 09:17 AM
Moo
Quote:

Originally Posted by 2clients
0
S x/sqrt(x+1) dx
-1
Any help would be greatly appreciated.

I tried setting:

u = x
du = dx
dv = 1/sqroot(x+1)
v = 2sqroot(x+1)

But everything is going to zero..

What's wrong ?

Using this integration by parts, you get :

$\displaystyle \int_{-1}^0 \frac{x}{\sqrt{x+1}} ~ dx=\left[uv\right]_{-1}^0-\int_{-1}^0 vdu$

$\displaystyle =\left[2x \sqrt{x+1}\right]_{-1}^0-\int_{-1}^0 2 \sqrt{x+1} ~ dx$

$\displaystyle =\left[2x \sqrt{x+1}\right]_{-1}^0-2 \int_{-1}^0 (x+1)^{1/2} ~ dx$

For the integral that's left, remember that $\displaystyle \int x^n ~ dx=\frac{x^{n+1}}{n+1}$
If you don't see what to do, substitute u=x+1

My final answer is something like $\displaystyle -\frac 43$