# Thread: Improper integral

1. ## Improper integral

Integral of 1/(sqrt(1-x)) from 0 to 1.

I am getting -2*sqrt(1-x) for the integral and then from 0 to 1 it would appear to be 0 - (-2) or 2 to be the answer?

2. Originally Posted by WartonMorton
Integral of 1/(sqrt(1-x)) from 0 to 1.

I am getting -2*sqrt(1-x) for the integral and then from 0 to 1 it would appear to be 0 - (-2) or 2 to be the answer?

$\lim_{\epsilon\rightarrow 0}\int\limits^{1-\epsilon}_0\frac{dx}{\sqrt{1-x}}=\lim_{\epsilon\rightarrow 0}\,-2\left[\sqrt{1-x}\right]^{1-\epsilon}_0=$ $\lim_{\epsilon\rightarrow 0}\,-2(\sqrt{\epsilon}-1)=2$