Favorite Integral: Gaussian or ∫(sin x)/x?

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In summary, the conversation revolved around the participants' favorite integrals, with one declaring the Gaussian Integral as their top choice and another sharing a list of their current favorite integrals. The discussion also touched on the topic of solving integrals and how preferences can change from day to day.
  • #1
FrancisD
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I do love the Gaussian Integral. It's a beautiful one for sure.

Also though,

∫(sin x)/x (over all space)

is a great one.
 
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  • #2
[itex]\int e^x dx[/itex]

Genius.
 
  • #3
Pengwuino said:
[itex]\int e^x dx[/itex]

Genius.
You would have that as your favorite integral xP

Hmm my favorite integral...it depends what I feel like doing...lol! I'll edit this later and think about this further.
 
  • #4
.




[itex]\int\frac{1}{\text{cabin}}dcabin \ = \ ? [/itex]




[itex]\text{log cabin plus sea}[/itex]
 
  • #5
The one I already solved :P
 
  • #6
http://www.2shared.com/document/D6szXApS/Integrals_from_R_to_Z.html

A list of my favourite integrals.

https://www.physicsforums.com/showpost.php?p=3433157&postcount=272

http://www.matematikk.net/ressurser/matteprat/viewtopic.php?t=24242&postdays=0&postorder=asc&start=0

http://www.artofproblemsolving.com/Forum/resources.php?c=87&cid=184

http://www.mathematica.gr/forum/viewtopic.php?f=9&t=7842&start=20

And just to top it of

[tex] \int \sin(\ln x) + \cos(\ln x) dx[/tex]
[tex] \int_{\mathbb{R}} \sin(x^2) + \cos(x^2) dx[/tex]
[tex] \int (2x^2+1)e^{x^2} dx[/tex]
[tex] \int \frac{x^2}{x^2+4x+8} dx[/tex]
[tex] \int \frac{x e^x}{(1+x)^2} dx[/tex]
[tex] \int \frac{x^{29}}{\left( 5x^2 + 49 \right)^{17}} dx[/tex]

But yeah, the list of my favourite integrals changes from day to day so :p
 
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  • #7

FAQ: Favorite Integral: Gaussian or ∫(sin x)/x?

What is an integral?

An integral is a mathematical concept that represents the area under a curve on a graph. It is often used to calculate the total value or quantity of something.

Why is it important to know your favorite integral?

Knowing your favorite integral can help you understand and apply mathematical concepts more effectively. It can also give insight into your problem-solving strategies and thought processes.

What factors influence your choice of favorite integral?

There are several factors that can influence a scientist's choice of favorite integral, such as the specific field of study, the complexity of the problem, and personal preference.

Can you give an example of your favorite integral and how it is used?

One example of my favorite integral is the definite integral, which is used to find the area under a curve between two specific points. This is commonly used in physics to calculate work, as the area under a force versus displacement graph represents the work done by that force.

What is the difference between an integral and a derivative?

An integral is the inverse operation of a derivative. While a derivative represents the instantaneous rate of change of a function, an integral represents the accumulation of that function over a given interval. In other words, a derivative tells us how quickly a function is changing at a certain point, while an integral tells us the total amount of change over a certain period of time.

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