strubenuff

My textbook's defines integration over a closed interval [a,b] where the limit an the norm approaches 0 exists, but the answer key claims f(x)=|x|/x can be integrated from -1 to 1. I realize the absence of a point at 0 has no effect on the area (points have no area), but then again, since it's made from an infinite number of points, the entire area of all functions should be 0...

strubenuff

I apologize for the double post; I didn't realize the administration had moved this.

Goliath

Strubenuff,

See my reply on your other thread on the integral of |x|/x on (-1,1). Essentially: yes, you can integrate on open intervals. For the easiest way to see why, think of it in terms of improper integrals. Just take the limit as t approaches a from the right of \int_t^b f(x) dx, or the limit as k approaches b from the left of \int_a^k f(x) dx.

Now, I really have to get back to grading! Let me know if you have any questions.

Sincerely,

Goliath