Decide whether or not the given integral converges

Question

Note: You may need to assume the fact that lim M→+ ∞ Mⁿe^−M = 0

 for all n.

Decide whether or not the given integral converges

-4

∫1/x^2dx

-∞

(a)Is the integral a convergent or divergent?

(b)If the integral converges, compute its value. (If the integral diverges, enter DNE.)

Answer 1

The integral quite clearly converges because you can calculate its value.

Let F(x) be the indefinite integral

F(x) = ∫dx/x² = -1/x + C

Then the definite integral is F(-4) - F(-∞) = -1/(-4) - 0 = 1/4.

But I do not know what is the relationship to the hint in the Note.