Simple question II

1. Dec 13, 2008

leopard

Is my book right to write

$$\int ^{0}_{- \infty}e^{-a|x|}dx = \int ^{0}_{- \infty}e^{ax}dx$$

?

In case, why?

2. Dec 13, 2008

mutton

If x is negative, what is |x|?

3. Dec 13, 2008

leopard

positive, but -a is still negative.

4. Dec 13, 2008

HallsofIvy

Staff Emeritus
That was not the question. If x is negative, then |x|= -x. For x negative, -a|x|= (-a)(-x)= ax.

5. Dec 13, 2008

gabbagabbahey

errmmm...maybe it's best to think of an example...suppose you have x=-2, what is |x|?

6. Dec 13, 2008

leopard

|-2| = 2

7. Dec 13, 2008

gabbagabbahey

Right, and if x=-2, what is -x?

8. Dec 13, 2008

leopard

Should be 2. I can simply put the minus outside the brackets?

9. Dec 13, 2008

gabbagabbahey

Well, if |x|=2 and -x=2, then surely you can say that |x|=-x?

So...what does that make -a|x|?