Question

Determine whether the improper integral converges or diverges, and find the value of each that converges.

∫^[infinity]_27 2/√x dx

Answer 1

It diverges.

Explanation:

We are given the integral:
`\int\limits^\infty_(27) (2)/(\sqrt x) dx`

`\int\limits^\infty_(27) (2)/(\sqrt x) dx= \lim_(t \to \infty) \int\limits^t_(27) (2)/(\sqrt x) dx=\lim_(t \to \infty) 4\sqrt x|^t_(27)=\infty-12\sqrt3=\infty`

So, it is divergent.