Find the result of this integration

In summary, the conversation discusses integration under the integral sign and how to utilize it to find the result of a specific integration problem. The conversation also touches on the use of LaTeX code to display mathematical formulae on the messageboard.
  • #1
Ali 2
22
1
Hi,
Find the result of this integration::
[tex]\int_0^\infty \frac { e^ {-3x} - e^ {-4x} }{x} dx [/tex]
The members who know the answer previously please don't answer in order to make the other members think :cool: !

Best wishes ,
 
Last edited:
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  • #2
My lips are sealed! :)
 
  • #4
Waiting .. :zzz: !
 
  • #5
That is differentiation under the integral sign, actually.

The answer is log(4/3).

How do you do mathematical formulae on the messageboard?
 
  • #6
Neat trick indeed, Benorin, this INTEGRATION under the integral sign. In this problem it involves the function [itex] e^{-ax} [/itex] seen as a function of 2 variables and one may use a theorem which allows changing the order of integration...

Daniel.
 
  • #7
Jesus! That's nice. Thanks. With regards to displaying math text, use LaTex code. There is a thread in the Math and Science Tutorials forum that describes it's use or you can just click on the "quote" button to see the code. Here, I'll write the relation suggested above:

[tex]\int_a^b dx \int_{\alpha_0}^{\alpha} f(x,\alpha)d\alpha=
\int_{\alpha_0}^{\alpha}d\alpha \int_a^b f(x,\alpha)dx[/tex]
 
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  • #8
Let me see,

[tex]
\newcommand{\mean}[1]{{<\!\!{#1}\!\!>}}
\newcommand{\braket}[2]{{<\!\!{#1|#2}\!\!>}}
\newcommand{\braketop}[3]{{<\!\!{#1|\hat{#2}|#3}\!\!>}}
\braket{\phi}{\psi} \equiv \int \phi^*(x) \psi(x)\,dx
[/tex]This LaTeX code doesn't work when I hit 'preview post'. There's no way to check it's right.
 
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  • #9
diracbracket said:
This LaTeX code doesn't work when I hit 'preview post'. There's no way to check it's right.

The preview has been on the fritz for some time now, so this is 'normal'. You can edit after you post of course.
 

1. What is integration?

Integration is a mathematical process of finding the area under a curve. It involves finding the antiderivative of a function and evaluating it over a given interval.

2. Why is it important to find the result of an integration?

Finding the result of an integration is important because it allows us to calculate various quantities such as distance, volume, and probability. It is also a fundamental tool in many fields of science and engineering.

3. How do you solve an integration?

To solve an integration, you need to first find the antiderivative of the function. This can be done by using integration rules and techniques such as substitution, integration by parts, and trigonometric identities. Once the antiderivative is found, you can evaluate it over the given interval to find the result of the integration.

4. What are some common integration mistakes to avoid?

Some common integration mistakes to avoid include not using the correct integration rule, forgetting to add the constant of integration, and making calculation errors. It is important to double-check your work and practice regularly to avoid these mistakes.

5. Can integrals be solved using a calculator?

Yes, integrals can be solved using a calculator. Most scientific and graphing calculators have built-in integration functions that can solve basic integrals. However, it is important to understand the concepts and techniques behind integration in order to use a calculator effectively and to check for any potential errors.

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