calculate this indefinite integral

Question

abb0t · Answer

I think I'm having a problem visualizing this question. Or mayb I need glasses.

anonymous · Answer

$$\int\limits_{?}^{?}e ^{|x|}$$

anonymous · Answer

@abb0t

anonymous · Answer

@KonradZuse

abb0t · Answer

You use the definition of absolute value: |x| = x if x >= 0, = -x if x < 0.

anonymous · Answer

so what do i do next? @abb0t now let's say x >= 0

abb0t · Answer

|dw:1358474469382:dw|

abb0t · Answer

You need to set some bounds. I posted the graph to maybe help you. I would say this is the graph? I think

abb0t · Answer

So maybe from 0 to infinity?

abb0t · Answer

Start by removing the absolute value by dividing the domain of the integration into regions where the absolute value in the integrand is definitely resolved.

In this case, over the domain (-∞,0]

So the absolute value in the integrand can be explicitly removed by replacing f(x) with
g(x) = exp(-x)
then solving the problem as usual.

anonymous · Answer

in this case does the "e" mean Euler's number or something else? cause this is confusing me.