# Improper Integrals

1. Feb 20, 2014

### rmiller70015

1. The problem statement, all variables and given/known data
$\int$ (x-2)-3/2dx

2. Relevant equations
$\int$f(x)dx from 0 to ∞ = lim (t$\rightarrow$∞) $\int$f(x)dx from 0 to t

3. The attempt at a solution
I have the solution from the solution manual, but I'm just not sure on one of the steps, after you substitute u=(x-2) and du=dx, then integrate u-3/2, but they say that the result to this step is lim(t$\rightarrow$∞) -2(x-2)-1/2, that is when they integrate u-3/2 they are getting a -2 coefficient, shouldn't it be a -2/3

2. Feb 20, 2014

### scurty

Try taking the derivative of the answer to see why it is a -2.

$\int x^n dx = \frac{1}{n+1} x^{n+1}, n \neq -1$

3. Feb 20, 2014

### rmiller70015

I'm ummm, I'm face palming right now, thanks.

4. Feb 20, 2014

### scurty

It's okay. Everybody has done something similar at one point or another!