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Two questions---nonevaluated Integrate; NIntegrate inside NDSolve

[Contact the author to obtain the notebook mentioned - moderator]

I have two questions about using Mathematica v3.0 to solve a problem I'm
working on.

1) An intermediate step involves a definite multiple integral that I
know can't be evaluated.  When I type in into Mathematica, it tries to
evaluate it and runs out of memory, at which point the kernel quits. 
I'd like to tell Mathematica not to try to evaluate the integral but to
leave it unevaluated.  How can I do this?  See the attached notebook

2) More important, I'd like to be able to numerically solve a
differential equation that involves a numerically evaluated integral.
See the attached notebook example2.nb for an example of what I'd like
to do.  How do I manage this?  It seems that I should be able to put
any numerically evaluatable function of y and y' into NDSolve and it
shouldn't complain.  How can I do this?

Thank you very much for the help.  I'm running Mathematica on a Mac
PowerPC 9500, system 8.5.

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