Hello All

1
I would like to thank for making this great program available, all the work that has been done!!


2
I am confronted with the problem of solving a double integral over a rectangle area...
basically id like to calculate an area of a rectangle, with the dxdy elements multiplied by the distance from the origin.

ex something like this:

int(int(sqrt(x^2+y^2))dx)dy

...i can get smath to show the double integral, but it keeps complaining that one of the variables is undefined.

Is this currently not solvable, because to get to the "outside" integral, some symbolic evaluation of sqrt(x,y) is necessary?

thanks for any help and best regards,

Mike Stamm

Um, that looks wrong.

I'd a thunk the area of a rectangle was more like something like

integral smally bigy integral small x bigx dx dy

rather than the scary thing you posted

Hi Greg

Im not worried about the f(x,y) function, im just interested in evaulating a double integral int(int(f(x,y)))dxdy, on AThis doesnt seem possible at the moment, correct?

I think the integral is correct by the way, i would like to weight the dA elements by the distance from center...

Mike

Ok, here is what I mean, illustrated with some pictures.

Why doesn't this work?

Mike

SMath File

Hello,

I think that the numerical integration incorporated in SMath is ment to solve the single definite integrals only. I think it is based on the numerical algorithms for the single definite integrals. Moreover, the SMath author - Andrey Ivashov - can give you more precise answer to this.

Regards,
Radovan

Hi.

It's simple. Numeric integration represented in SMath Studio by int(..) function, this function uses Simpson method to integrate. When you write double integral using int(int()) then SMath Studio first of all tries to solve most prioritized operation - inner int(..)... but it is impossible, because function to integrate has two variables - this is not a behavior of simple Simpson. So, as a result, program shows an error, that one of the variables is undefined.

Please, use special numerical methods for double integral solving.

Best regards, Andrey Ivashov.

Hello Radovan and Andrey

Thank you for the explanations.

Does Smath have "special numerical methods" for solving dbl integrals built-in? If not, will it in the future?

Best Regards

Mike Stamm

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For example, Maxima has the "dblint" function available, as follows:

If the variables can be separated, SMath can do multiple integrals in symbolic mode.

** sorry about the confusing spaces below, the forum interpreter evaluated some ( as smilies when typed without spaces.


example: to evaluate


int ( int ( ab ) da ) db

write it as

int ( b * int ( a ) da ) db

and select symbolic for the optimization mode

(Only the integral needs to be in symbolic mode. The rest of the worksheet can be evaluated numerically if that speeds calculation.)

If a numeric answer is needed, write as follows with symbolic optimization for the first line and numeric optimization for the second:

ans := int ( b * int ( a ) da ) db
ans =

To integrate something like sqrt ( a+b ), a variable substitution can sometimes be used to convert to a single variable, depending on the nature of the problem.

This is what Maxima does.

Edit: the second integral can be simplified using one of the many Maxima simplification functions.

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