# Thread: comparison test for improper integrals

1. ## comparison test for improper integrals

I have to use the comparison test to determine if the integral diverges or converges but I am confused about how to do this. Please help.

integral from 1 to infinity of dx/(square root(x^4 + 4x^3))

2. This was posted before, anyway, for $x\ge1$ it's $\frac{1}{\sqrt{{{x}^{4}}+4{{x}^{3}}}}\le \frac{1}{\sqrt{{{x}^{4}}}}=\frac{1}{{{x}^{2}}},$ so your integral converges by direct comparison with $\int_1^\infty\frac{dx}{x^2}.$

3. okay so if the bounds change to from 0 to 1 it would be divergent?