Is my book right to write

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

?

In case, why?

 

Remembering that exp(x) and exp (-x) are mirror image functions and that both are positive definite you should be able to see that the dotted area is your first integral and the shaded one the second.

 

boks,

Is my book right to write



?

In case, why?

For the same reason that -a|x| = -a(-x) = ax when x <= 0, which is the range of the integral. In other words |x| = -x when x is negative or zero.

Ratch