How to Specify an Interval in Mathematica for the Integrate Function?

In summary, the conversation discusses using Mathematica's Integrate function and how to specify a specific interval for the integration. The solution is to use the Assuming function with the appropriate conditions. The conversation also touches on the importance of parameters in integrals and how they can affect the convergence of the integral.
  • #1
BCox
16
0
Hello:

I would like to use Mathematica Integrate function. But how do I specify the following interval

(0 , Pi/2 ]

?

When I write

L \[Element] (0, Pi/2]

It simply bolds ( and ] in orange in error.

How do I get Mathematica to recognize that for the integrand, my value L is in (0, Pi/2]?
 
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  • #2
Try this:

Code:
Assuming[{L>0&&L<=pi/2},Integrate[...]]
 
  • #3
i don't understand how including 0 in your integration would change the answer anyhow.. its an integration!
 
  • #4
elduderino said:
i don't understand how including 0 in your integration would change the answer anyhow.. its an integration!

I don't think he is integrating over [itex]L[/itex]. I think [itex]L[/itex] is a parameter that occurs in the integrand, and its value affects whether the integral converges, and to which value.

A simple example is the integral

[tex]\int_0^{\infty}e^{-kx}dx[/itex]

which only converges for [itex]k>0[/itex]
 
  • #5
gabbagabbahey said:
I don't think he is integrating over [itex]L[/itex]. I think [itex]L[/itex] is a parameter that occurs in the integrand, and its value affects whether the integral converges, and to which value.

A simple example is the integral

[tex]\int_0^{\infty}e^{-kx}dx[/itex]

which only converges for [itex]k>0[/itex]

Yes, exactly. L pertains to the integrand.
 

1. What is the syntax for specifying an open interval in Mathematica?

The syntax for specifying an open interval in Mathematica is (a, b), where a and b are the lower and upper bounds of the interval, respectively. This notation indicates that the interval includes all values greater than a and less than b.

2. How do I specify a half-open interval in Mathematica?

To specify a half-open interval in Mathematica, use the notation (a, b] or [a, b), depending on whether you want the interval to include the lower or upper bound, respectively. For example, (-∞, 5] represents all values greater than negative infinity and less than or equal to 5.

3. Can I specify an open interval with infinite bounds in Mathematica?

Yes, you can specify an open interval with infinite bounds in Mathematica by using the notation (-∞, ∞). This represents all real numbers.

4. How do I specify multiple open intervals in Mathematica?

You can specify multiple open intervals in Mathematica by using the Union function. For example, if you want to specify the intervals (1, 3) and (5, 7), you would use the syntax Union[(1, 3), (5, 7)].

5. Is it possible to specify an open interval that includes only integers in Mathematica?

Yes, you can specify an open interval that includes only integers in Mathematica by using the Integers function. For example, (-∞, ∞) ∩ Integers represents all integers.

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