Why hello improper integral, how are you?

[yeahyeah<3]

Homework Statement

integral from -1 to 1 of 3/x^2 dx

Homework Equations

The Attempt at a Solution

Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

Limit
t-> infinity -3/t - (-3/-1) + Limit t--> inifinty (-3/1) - (3/t)

-3 -3 = -6

Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?
Thanks so much =]

 

[D H]

Why infinity? It is (a) outside the domain, and (b) you are integrating across the singularity.

 

[Citan Uzuki]

Now when I check the answer in my calc I get infinity. Thus my answer is probably wrong. Where did I go wrong?

Limit
t --> infinity integral from -1 to t of 3/x^2 dx + limit t --> infinity integral from t to 1 of 3/x^2 dx

This should be as t→0.