Intergrating a derivative of absolute value in exponential

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Homework Help Overview

The discussion revolves around an integral problem involving the derivative of an exponential function that includes an absolute value term. The integral is defined over the range from negative infinity to positive infinity, with the variable x as the independent value.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the nature of the integrand, questioning how to handle the absolute value in the context of integration. Some suggest rewriting the integrand to eliminate the absolute value, while others propose breaking the integral into two parts to address the piecewise nature of the function.

Discussion Status

The discussion is ongoing, with participants offering guidance on potential techniques for integration and questioning the properties of the constants involved. There is no explicit consensus yet, but various approaches are being considered.

Contextual Notes

There is a question regarding the positivity of the constant involved in the integral, which may influence the approach taken. The original poster has not provided all necessary details about the constants or the specific form of the integrand.

myoikos
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hey~ folks!

i'm in trouble with this integral problem.

the range of the integral is from -∞ to ∞ and it has x as independent value.

and the integrand is a derivative of absolute value in exponential;

∫[itex]^{∞}_{-∞}[/itex] (d/dx e[itex]^{-a|x|}[/itex])dx

any idea for the problem??
 
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myoikos said:
hey~ folks!

i'm in trouble with this integral problem.

the range of the integral is from -∞ to ∞ and it has x as independent value.

and the integrand is a derivative of absolute value in exponential; e[itex]^{a|x|}[/itex]

any idea for the problem??
Welcome to Physics Forums.

What is the definition of the absolute value function? Can you think of a way to re-write the integrand without the absolute value sign?
 
Use a technique like one might use when integrating other piecewise functions; that integral can be expressed as the sum of two definite integrals.
 
Is the constant, α, positive ?
 

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