Thread: Sketch the region and find the area

Sketch the region between -1 and 1 for 1/x^2 and find its area.

So this is integral (-1 to 1) 1/x^2

I can compute this and it comes to -2, but it is not integrable at x=0. So should I put for the area that is is infinite or what would the area be?

Originally Posted by zhupolongjoe

Sketch the region between -1 and 1 for 1/x^2 and find its area.

So this is integral (-1 to 1) 1/x^2

I can compute this and it comes to -2, but it is not integrable at x=0. So should I put for the area that is is infinite or what would the area be?

you said it, it's not integrable there because it's not bounded on

this splits as then work this to see what leads to.

But you also get when you do that, for example in the first integral

-1/x and you can't plug 0 into there...so that brings me back to the question...is it just infinite area?

Try splitting the integral into two and substituting the variable.

So:


Substitute the lower limits of integration with variables, and take the limit as those variables approach zero from the left and right respectively.

Still get division by 0

Not if you take the limit as some variable approaches zero from the right or left. Then you will get infinity.