Question

Determine whether the integral is convergent or divergent? integral from 3 to infinity 3dx/ (x^4 +3)^1/3

Answer 1

I think this should be done using comparison theorem?

Answer 2

http://www.wolframalpha.com/input/?i=integrate+3%2F%28x%5E4%2B3%29%5E%281%2F3%29+dx+for+3+to+infinity&a=%5E_Real

it converges, the function converges to 0 as x goes to infinity, so the area under curve converges

Answer 3

I don't need to evaluate it, I assume I have to compare it to the integral that is smaller or larger and if that one is conv/ diverg, the original should be same