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

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SUMMARY

The integral of e^(-|x|) can be calculated by evaluating the cases for x < 0 and x > 0 separately. This approach mirrors the integration of e^(-x) and e^(x), but requires careful consideration of the absolute value function. The integral can be expressed as two distinct parts: ∫ e^(-x) dx for x ≥ 0 and ∫ e^(x) dx for x < 0. This method ensures accurate results without the use of a calculator.

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  • Understanding of basic calculus concepts, particularly integration.
  • Familiarity with the properties of exponential functions.
  • Knowledge of absolute value functions and their implications in calculus.
  • Ability to evaluate definite and indefinite integrals.
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  • Study the integration techniques for piecewise functions.
  • Learn about the properties of the exponential function in calculus.
  • Explore the concept of improper integrals and their applications.
  • Practice solving integrals involving absolute values in various contexts.
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Students studying calculus, mathematics enthusiasts, and anyone looking to enhance their integration skills, particularly with exponential functions and absolute values.

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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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