Question

My question relates to Problem 3E-2 (b) in the integration problem set. I understand the 2nd part of the question (why lim as x approached -inf of E(x) is - lim as it approached +inf) but why then isn't the answer to the first part 0 (isn't it essentially asking for the sum of the +inf and neg inf limits of E(x)?

Answer 1

Recall that if the integral from a to b = c, then the integral from b to a = -c. Same function, same interval, but going in the opposite direction so we get the opposite sign.

In the second part of this problem (3E-2(b)) we are in effect looking at the integral from 0 to -infinity, which produces a negative number. In the first part of the problem we are in effect looking at the integral from -infinity to +infinity. You're misinterpreting the "left half" of this integral, which is the integral from -infinity to 0. We're going in the opposite direction here from when we do the second part of the problem, and that means it's positive because the second part, going from 0 to -infinity, was negative.

Answer 2

Thanks, I wrote out the problem more carefully (a lesson) and it was obvious.