Determine whether the improper integral converges or diverges, and find the value of each that converges.
∫^[infinity]_27 2/√x dx

Respuesta :

Answer:

It diverges.

Step-by-step explanation:

We are given the integral: [tex]\int\limits^\infty_{27} \frac{2}{\sqrt x} dx[/tex]

[tex]\int\limits^\infty_{27} \frac{2}{\sqrt x} dx= \lim_{t \to \infty} \int\limits^t_{27} \frac{2}{\sqrt x} dx=\lim_{t \to \infty} 4\sqrt x|^t_{27}=\infty-12\sqrt3=\infty[/tex]

So, it is divergent.