# How do you evaluate the integral #int e^(-absx)# from #-oo# to #oo#?

2

graph{e^(- | x|) [-10, 10, -5, 5]}

use the symmetry so that it becomes

2

here

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To evaluate the integral ∫e^(-|x|) from -∞ to ∞, you can split the integral into two parts: from -∞ to 0 and from 0 to ∞. In each part, the absolute value function can be removed by considering the different cases of x being negative or positive. After integrating each part separately, you will arrive at the result of 2.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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