Integral using integral tables

  • Thread starter eku_girl83
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In summary, the integral of x^2 * e^(-2*a*x^2) with respect to x as x ranges from 0 to infinity can be evaluated using integration by parts or substitution. The resulting integral is similar to the form of \int^{\infty} _{0} x^{p} e^{-bx^{2}} dx, which can be found in integral tables.
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eku_girl83
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Evaluate the integral of x^2 * e^(-2*a*x^2) with respect to x as x ranges from 0 to infinity.

I can't find anything in the integral tables that match this exactly...Can someone help me out?
 
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  • #2
eku_girl83 said:
Evaluate the integral of x^2 * e^(-2*a*x^2) with respect to x as x ranges from 0 to infinity.

I can't find anything in the integral tables that match this exactly...Can someone help me out?

That looks like a straightforward substitution to me.

Sorry. misread the integral.. thougt it was 2xe^...

Try using integration by parts - [itex]x^2 e ^{-2ax^2}=x \times xe^{-2ax^2}[/itex]
 
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  • #3
integrate by parts or chage variables and let [tex] 2a = b [/tex], I'm sure there is a listing for
[tex] \int^{\infty} _{0} x^{p} e^{-bx^{2}} dx [/tex].
 

What is an integral table?

An integral table is a reference tool used by mathematicians and scientists to find the antiderivatives of various functions. It contains a list of commonly used integrals and their corresponding solutions.

How do you use an integral table to solve integrals?

To use an integral table, you first identify the function you want to integrate. Then, you find the corresponding integral in the table and substitute the values into the solution. Finally, you simplify the solution to get the final answer.

What is the purpose of using an integral table?

The purpose of using an integral table is to simplify the process of solving integrals. It can save time and effort by providing a quick reference for commonly used integrals.

How accurate are the solutions provided in an integral table?

The solutions in an integral table are accurate, but they may not be applicable to all cases. It is important to check for any special cases or conditions that may require a different approach.

Are there any limitations to using an integral table?

Yes, integral tables may not contain every possible integral and may not be applicable to all functions. They are best used for commonly used integrals and may not be suitable for more complex integrals.

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