# Math Help - Converge or Diverge

1. ## Converge or Diverge

Does $\int_{0}^{2}\frac{x}{\sqrt{4-x^2}}dx$ converges or diverge? If it converges, evaluate the integral.

2. Originally Posted by Yogi_Bear_79
Does $\int_{0}^{2}\frac{x}{\sqrt{4-x^2}}dx$ converges or diverge? If it converges, evaluate the integral.
This is an Improper integral of the Second Type.
There is a vertical asymptote at $x=2$
Thus, you need to find,
$\lim_{t\to 2^-}\int_0^t \frac{x}{\sqrt{4-x^2}} dx$
Use inner functional substitution,
$u=4-x^2$
Thus,
$\lim_{t\to 2^-} -(4-x^2)^{1/2}|_0^t=-(4-t^2)^{1/2}+(4-0^2)^{1/2}=2$