Quick Integration Question w/ e

  • Thread starter Weather Freak
  • Start date
  • Tags
    Integration
In summary, the conversation is about solving the integral \int (1/e^z) dz and determining the correct answer. The questioner initially thought it was ln (e^z) = z but their TI-89 calculator gave them -e^-z as the answer. The expert clarifies that the correct answer is -e^-z + C and explains how to arrive at this solution. The questioner thanks the expert for their help and acknowledges that the question was odd to begin with.
  • #1
Quick Integration Question w/ "e"

Hey folks,

On my calc homework tonight, I have to solve the integral [tex]\int (1/e^z) dz[/tex] as part of my differential equation. Anywho, I thought the answer to that was [tex]ln (e^z) = z[/tex] but my TI-89 claims that it's really [tex]-e^-z[/tex].

Could someone please tell me which of us is correct, and more importantly, why? I was under the impression that the antiderivative of e was simply itself if there was no inner function (and since z is just a variable, I don't think there is).

Thank you!
 
Physics news on Phys.org
  • #2
I'm a little confused by your question but:

[tex]\int \frac{1}{e^z}dz = \int e^{-z} dz = -e^{-z} + \mathcal{C}[/tex]
 
  • #3
Zurtex said:
I'm a little confused by your question but:

[tex]\int \frac{1}{e^z}dz = \int e^{-z} dz = -e^{-z} + \mathcal{C}[/tex]

Oh, wow. I didn't even think of it like that, thank's a lot! Yeah, the question does seem odd now that I know the answer.
 
  • #4
Your calc. was right this time, your answer was incorrect. You should remember that you can differentiate to check and [tex]D_x(ln(e^z))[/tex] is just [tex]1[/tex].
 

What is Quick Integration Question w/ e?

Quick Integration Question w/ e is a method used in mathematics and computer science to quickly solve integration problems by using the variable "e" as a constant.

How does Quick Integration Question w/ e work?

To use Quick Integration Question w/ e, you first need to identify the variable "e" in the given integration problem. Then, you replace the variable with the constant "e" and integrate as usual. The result will be the same as if you had integrated with the variable included, but it can save time and effort in certain cases.

When should I use Quick Integration Question w/ e?

Quick Integration Question w/ e is most useful when the integration problem involves a function that includes the variable "e" in the exponent. It can also be helpful when the function is in the form of an exponential or logarithmic function.

Are there any limitations to using Quick Integration Question w/ e?

While Quick Integration Question w/ e can be a useful tool, it may not work for all integration problems. It is important to carefully consider the given problem before deciding to use this method.

Can Quick Integration Question w/ e be used for indefinite integrals?

Yes, Quick Integration Question w/ e can be used for both definite and indefinite integrals. However, it may be more beneficial for definite integrals as they tend to involve simpler functions.

Suggested for: Quick Integration Question w/ e

Replies
2
Views
468
Replies
2
Views
923
Replies
1
Views
825
Replies
2
Views
643
Replies
25
Views
857
Replies
20
Views
369
Replies
4
Views
926
Back
Top