Expert: Paul Klarreich - 1/28/2010

Question
Evaluate the following integral:
{1
| (sqrt(t))/(t+1)
}0

For this I tried substituting u=t, u=sqrt(t), u=t+1
I didn't get the answer for any of these substitutions, and I'm not sure how to do this.

Answer
Questioner: mike
Country: United States
Category: Calculus
Private: No
Subject: definite Integrals using Substitution
Question: Evaluate the following integral:
{1
| (sqrt(t))/(t+1)
}0

For this I tried substituting u=t, u=sqrt(t), u=t+1
I didn't get the answer for any of these substitutions, and I'm not sure how to do this.
.........................................................
First:  Don't leave out the  dx, or dt, or whatever. In the future, I'll just send them back for correction.

Try a 'rationalizing substitution':

u = sqrt(t)

u^2 = t

2u du = dt

{1
| (sqrt(t))/(t+1) DT DT DT DT !!!!!!
}0

{1
| [u/(u^2+1)] 2 u du
}0


{1
| [2u^2/(u^2+1)] du
}0

Take it from there.  [Use long division.]