Integrating a complex function

C

Calcperson

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Oct 14, 2006
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Hey,

I do not know how to solve this at all...

I need to find integrate of this function

F(x)=(1/[the squareroot of 2pi]theda) times e to the ((x-mu)^2)/(2(theda^2))

mu=mean and I think I wrote down theda=itderiv?

Thanks
 
The function \(\displaystyle e^{x^2 }\) has no simple antiderivative. It takes advanced methods:

\(\displaystyle \L
\int {e^{x^2 } dx = \frac{{ - 1}}{2}i\sqrt \pi erf\left( {ix} \right)\quad ,\quad erf(z) = \frac{2}{{\sqrt \pi }}\sum\limits_{n = 0}^\infty {\frac{{\left( { - 1} \right)^n z^{2n + 1} }}{{n!\left( {2n + 1} \right)}}} } .\)
 
Calcperson said:
how can i use that for my question?
Click to expand...
Wasn't your question "integrate the following"...? Or was what you posted only part of some other exercise, so the integral itself may be incorrect...?

Thank you.

Eliz.
 
hey actually I think I may have gotten it wrong this is the function to integrate

1/(2pi)^.5 * e^((x-m)^2/(2s^2)

where m is the mean and s^2 is the variance

thanks! sorry if i ever sound snappy!
 
No, that is exactly the same problem you posted the first time. You still seem to think that is an easy Calculus II type answer for the problem. That is simply not the case.
This is such a well-known problem. Anyone with a modicum experience recognizes it as the integral of the probability distribution for the normal random variable. There is no simple antiderivative that is why the ERF function was derived using complex variable theory to handle this very difficult integral. Almost any advanced calculator or a computer algebra system will have built in tables to help you lookup particular values for the integrals. Computer algebra systems will evaluate the numerical integral for you. What a CAS will not do is give a anything but the ERF function as a representation of the integral.
 
Calcperson said:
can we still try to solve it...even if it is really complex?
Click to expand...
It might be helpful if you reviewed the replies you've received thus far, which explain that there is no way to do what you're asking. You can either use the complex form of the solution, or the numerical methods, but there is no simple solution. The solutions that you have already been given are all there is.

I apologize for any confusion. I hope this clarifies the issue in your mind.

Eliz.
 
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Do you have a graphing calculator the will do integrals?
If so, you can put the function into the calculator and evaluate it.
The above was done with a CAS. The function has mean 3 and SD 2.
But that is what we mean by there being no ‘calculus solution’ to it.
 
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