What am I doing wrong with this simple integral?

[Physics_wiz]

I want to integrat x^-2 between -1 to 1. The answer shouldn't exist (should probably be something divided by 0) because the area is infinite between -1 to 1. But I integrate, and I get -x^-1 from -1 to 1. I then plug the bounds in and I get: [-(1)^-1] - [-(-1)^-1] which is -1 -1 or -2. What am I doing wrong?

 

[vsage]

because the area is infinite between -1 to 1

Not true. You're right with your answer. One thing you will learn with integrals is that an infinite jump at any particular point in a function f(x) may correspond to a finite jump in its integral.

 

[Physics_wiz]

Not true. You're right with your answer. One thing you will learn with integrals is that an infinite jump at any particular point in a function f(x) may correspond to a finite jump in its integral.

Why is the answer negative? I attached a picture of the graph, it still looks like it should be infinite to me.

 

[vsage]

Ok my apologies. You were correct in your arithmetic, but your answer is complete garbage. As far as I know you cannnot integrate over that interval. There are however cases where a function "blows up" but has a finite integral, so you must be careful (the only case I know of however is the dirac delta function, whose integral is 1 over infinite limits)