Question

I have an extra negative in this problem, and I can't figure out why it shouldn't be there:
Evaluate the improper integral:

Answer 1

\[\int\limits_{-\infty}^{\infty}e ^{-x}dx\]

Answer 2

That integral does not exist. Perhaps you meant \((0,\infty)\)? Definitely no good for \(x<0\).

Answer 3

Nope

Answer 4

I have to break it at 0 and take the limit

Answer 5

I got it down to lim(a->-infinity)(-1)+(1/(e^a)) + lim(b->infinity)(-1/(e^b))+1

Answer 6

But apparently, I have a negative in the first limit that isn't supposed to be there

Answer 7

Here is someone's solution http://www.slader.com/textbook/9780132014083-calculus-graphical-numerical-algebraic-3rd-edition/467/exercises/21/

Answer 8

that has an absolute value...yours doesn't...big difference

Answer 9

The actual problem in the book doesn't have an absolute value, but it still has the same answer that he got

Answer 10

the integral you wrote above does not converge

Answer 11

the one with the absolute value does converge

Answer 12

Oh snap it actually does have absolute value bars around the x. They are really faint, but they are there

Answer 13

so its e^-lxl

Answer 14

I think it didn't print well in my copy of the book

Answer 15

Now I really have no idea what to do

Answer 16

you just posted a link to a solution. how can you have no idea what to do?

Answer 17

I dont understand what he did. Although the right side of my solution is the same as his