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5

The problem is the ByteCount of H is ~630 KB, so Simplify will run forever. ComplexExpand[ With[{z = x + I y}, E^-Sqrt[z^2]/(Sqrt[z^2]+Sqrt[z^2] Cosh[Sqrt[z^2]]+Sqrt[z^2] Sinh[Sqrt[z^2]]) ] ] // ByteCount (* 629392 *) Here are two partial workarounds. I call these workarounds because it proves H is not analytic, but it doesn't derive it i.e. we ...

2

I think I solved this problem. The error message was due to the fact that Mathematica cannot perform the internal integration, so I split the two integrations and used NIntegrate instead of the symbolic integration: p[z1_?NumericQ, R_?NumericQ, z_?NumericQ] := -NIntegrate[ BesselK[0, x/Ld]*x* ArcSin[(2*x)/( Sqrt[(z1)^2 + (x + 7.6)^2] + ...

2

Now in V10 we have ImplicitRegion and RegionCentroid to do this easily: reg = ImplicitRegion[y > 0 && y <= 1 - x^2/4, {x, y}]; Then: RegionCentroid[reg] {0, 2/5}

2

This is a very nice problem. If I may dispense with the notation for random variables as $f$ and $k$, and refer to them instead as $X$ and $Y$ ... The Problem Let $X \sim Uniform(0,1)$ and $Y \sim Uniform(2,5)$ be independent random variables, with joint pdf $f(x,y) = \frac13$: f = 1/3; domain[f] = {{x, 0, 1}, {y, 2, 5}}; We seek a closed-form ...

1

Tweak Solution Since Seth has provided 2 answers, I thought I might also put up another answer. My motivation for separating this from my original answer is that ... my original answer is a self-contained mathematical solution in transformations of random variables, essentially striving to side-step Mathematica's use of Boole which was not working, ...

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