This is one heck of an embarrassment but it is impressive exactly how these bits of subtlety gets lost in the earlier of the head after the initially year of undergraduate studies-with eexceptionally computation chucked into brianowens.tvematica.

You are watching: Integral of e^abs(x)

Here goes, I"m trying to incorporate $int_-infty^+inftye^ x ideal e^-ikxdx$

As usual, absolute value is somepoint to be wary of.

I spilt the integral down to the negative and positive x domajor to account for the $|x|$.

Then, we have

$int_-infty^0e^-aleft ( -x appropriate )e^-ikxdx+int_0^+inftye^-axe^-ikxdx$

or maybe, by symmeattempt,

$2int_0^+inftye^-axe^-ikxdx$

Have I nailed this?


integration definite-integrals improper-integrals indefinite-integrals absolute-worth
Share
Cite
Follow
edited Jan 4 "16 at 5:07
brianowens.tvematicing
asked Jan 4 "16 at 5:05
*

brianowens.tvematicingbrianowens.tvematicing
5,40966 gold badges5252 silver badges102102 bronze badges
$endgroup$
0
Add a comment |

1 Answer 1


Active Oldest Votes
4
$egingroup$
This was correct prior to the edit; the expression

$$int_-infty^0 e^-a(-x) e^-ikx , dx + int_0^infty e^-ax e^-ikx , dx$$

was correct, yet it is not equal to $2 int_0^infty e^-ax e^-ikx , dx$. Rather, the first integral above is

eginalign*int_-infty^0 e^ax e^-ikx , dx = int_0^infty e^-ax e^+ikx , dxendalign*

Keep in mind the sign on the exponential is various.

As an error inspect, note that the Fourier transform of an also feature is actual. If you compute the integral $int_0^infty e^-ax e^-ikx , dx$, you carry out not acquire a actual attribute.


Share
Cite
Follow
answered Jan 4 "16 at 5:12
user296602user296602
$endgroup$
Add a comment |

Your Answer


Thanks for contributing an answer to brianowens.tvematics Stack Exchange!

Please be sure to answer the question. Provide details and share your research!

But avoid

Asking for assist, clarification, or responding to other answers.Making statements based on opinion; back them up via referrals or personal endure.

Use brianowens.tvJax to format equations. brianowens.tvJax reference.

To learn even more, view our tips on creating excellent answers.

See more: Cyberpunk Deus Ex Human Revolution Character Concept Art & Game Info


Draft saved
Draft discarded

Sign up or log in


Sign up utilizing Google
Sign up utilizing Facebook
Sign up making use of Email and Password
Submit

Article as a guest


Name
Email Required, however never shown


Blog post as a guest


Name
Email

Required, but never shown


Article Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy


Not the answer you're looking for? Browse various other questions tagged integration definite-integrals improper-integrals indefinite-integrals absolute-value or ask your very own question.


Featured on Meta
*

23 votes · comment · stats
Related
0
Integrating absolute value function
1
Integrating an absolute value on exponential
0
Integrating absolute terms
2
Integrating this tricky integrand also
0
Absolute worth in integrating element
0
Get absolute value in exponent of integrand
1
Integrating a regular absolute worth function through exponential
Hot Netjob-related Questions even more warm questions

Concern feed
Subscribe to RSS
Concern feed To subscribe to this RSS feed, copy and paste this URL right into your RSS reader.


*

brianowens.tvematics
Company
Stack Exreadjust Network
site design / logo design © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. rev2021.9.9.40167


brianowens.tvematics Stack Exadjust functions best via JavaScript enabled
*

Your privacy

By clicking “Accept all cookies”, you agree Stack Exadjust deserve to save cookies on your gadget and also discshed information in accordance with our Cookie Policy.