Calculate Integral of e^(-|x|) Without a Calculator

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To calculate the integral of e^(-|x|) without a calculator, it is necessary to consider two cases: x < 0 and x > 0. For x < 0, the integral simplifies to ∫ e^x dx, while for x > 0, it becomes ∫ e^(-x) dx. Each case can be solved using standard integration techniques. The final result combines the solutions from both cases. Understanding the behavior of the absolute value function is key to solving this integral correctly.
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How do I calculate the intergral of e^(-|x|) ("e to the minus absolute value of x") without a calculator?
 
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welcome to pf!

hi reidwilson! welcome to pf! :smile:

(try using the X2 icon just above the Reply box :wink:)
reidwilson said:
How do I calculate the intergral of e^(-|x|) ("e to the minus absolute value of x") without a calculator?

same way as ∫ e-x dx or ∫ ex dx,

except you need to do the cases of x < 0 and x > 0 separately :wink:​
 

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