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Dear All,
Sorry perhaps for a sillylooking question from someone who does not have very strong math skills.
In the attached pdf file, I describe a problem which I have been trying to unsuccessfully crack after trying a few manipulations.
Some intuitive thoughts are as follows: the inner two integrals over dy and dd give an area. Perhaps that area depends only on the "height" m. Suppose this area is a sheet of density 1/unit area. The final goal is to integrate E^area over dm.
Is the integral of exponential area of unit density/area = integral of unit area of exponential density/area? Can we pull that exponential "through" the integration?
Any other suggestions helping to transform (1) into a triple integral are highly appreciated.
Thanks a lot.
Anna.
P.S. This is not a h/w question, it is for my own research.
Sorry perhaps for a sillylooking question from someone who does not have very strong math skills.
In the attached pdf file, I describe a problem which I have been trying to unsuccessfully crack after trying a few manipulations.
Some intuitive thoughts are as follows: the inner two integrals over dy and dd give an area. Perhaps that area depends only on the "height" m. Suppose this area is a sheet of density 1/unit area. The final goal is to integrate E^area over dm.
Is the integral of exponential area of unit density/area = integral of unit area of exponential density/area? Can we pull that exponential "through" the integration?
Any other suggestions helping to transform (1) into a triple integral are highly appreciated.
Thanks a lot.
Anna.
P.S. This is not a h/w question, it is for my own research.
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