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Double integration of a complex function

Orpita Saha, University of Utah
Posted 5 months ago

Hi, I want to do the double integration of the following function:

Integrate[(-1)*(x + l/2)/((x + l/2)^2 + (y - y1)^2 + (z - z1)^2)^(3/2),{y1, 1,2},{z1,3,4}]

But, I am not getting any results. Mathemetica is saying the following things
"This computation has exceeded the time limit for your plan.\

$Aborted.

I have attached the screenshot of this here.
Any suggestions regarding solving this complex double integral will be appreciated. Thanks.

Attachment

Attachments:
mathematica error.png
POSTED BY: Orpita Saha
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Mathematica have trouble to compute this integral:

POSTED BY: Mariusz Iwaniuk

Thank you for being so helpful. After doing the double integration over y1 and z1, I need to do triple integration over x,y and z (dx, dy and dz). I tried to do that. I got output for integration over x but did not get any output over y and z. I am not sure why. It might be low memory or something like that.

Another problem: My real limits are y1max = 0.0019 and y1min = -0.0019, z1max = 1.15*10^-5 and z1min = -1.15*10^-5. If I use those limits, I can not get any output over integration dz1. I am attaching my pdf files here. Real limits for x, y and z are xmin = -0.006, xmax = 0.006 ymin = -0.0019, ymax = 0.0019 z_min = -1.2510^-04, z_max = 1.2510^-4 I really appreciate any help you can provide. Thank you.

Attachments:
real limit complexity.pdf
triple integrati...pdf
POSTED BY: Orpita Saha

Your integral is 5D.

Why do you expect that there is a closed form solution?

Not all integrals can be expressed in closed form.

Probably only way is compute numerically.

POSTED BY: Mariusz Iwaniuk

Thanks. Got it.
POSTED BY: Orpita Saha
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