Thread: Sketch the region and find the area

1. 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?

2. 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 $[-1,1].$

this splits as $\int_{-1}^0\frac{dx}{x^2}+\int_0^1\frac{dx}{x^2},$ then work this to see what leads to.

3. 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?

4. Try splitting the integral into two and substituting the variable.

So:
$\int_{-1}^0\frac{dx}{x^2}+\int_0^1\frac{dx}{x^2},
$

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

5. Still get division by 0

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