# Math Help - does this integral converge?

1. ## does this integral converge?

integral( x^p * exp(-x^q)dx, 0,infinite) where, p,q >0

2. Yes it does. Can't remember why though.

3. Yep, it converges.

$\int_0^{\infty}x^p\cdot{e^{-x}}dx=\Gamma(p+1)$

To see why it converges, compute the limit $\lim_{x\rightarrow{+\infty}}\frac{x^p\cdot{e^{-x^{q}}}}{\frac{1}{x^2}}$
What can you say about $\int_1^{\infty}{\frac{dx}{x^2}}$? and then what happens with $\int_1^{\infty}{x^p\cdot{e^{-x^{q}}}dx}$ ?