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?
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?
Try splitting the integral into two and substituting the variable.
So:
$\displaystyle \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.