Finding convergence or divergence of an integral?

Question

Hello, I've been really struggling on determining the convergence/divergence of this integral with strong evidence. I have to use a test of some sort to show evidence, such as the Integral Test, but I have been having troubles deciding if this test is the best... If there's anyone good with Calc II, I could really use some guidance. This is the last problem on my homework set that I am stuck on.

Answer 1

The integral converges. Set x^2 = t

Source(s): The integral converges. Set x^2 = t then 2xdx = dt or 2dx = dt/sqrt(t) So I = 2 integral [0 to oo] 2e^-x^2 dx = sqrt(pi) See this https://www.youtube.com/watch?v=hAxlK8W80Mg