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2

You are having round-off problems. One way to eliminate them is by replacing your approximate real numbers by rational numbers, because Mathematica computes results with exact numbers to arbitrary precison. c = 3*10^(8); h = 105*10^(-36); m = 911*10^(-33); r = h/(m*c); a = 730*10^(-5); Then, both normalized integrals yield precisely 1.

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You can also use Solve Solve[Integrate[ (x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, v}] == 50, v, Reals][[1]] // Quiet {v -> 12.9905}

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s[v_?NumericQ] := NIntegrate[(x^2 - .0015 x^4)/D[(x^2 - .0015 x^4), x], {x, 1.414, v}] FindRoot[s[v] == 50, {v, 11}] (* {v -> 12.9905} *)

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Alternatively, use FindRoot FindRoot[Integrate[ SquareWave[{0.2, 0}, ((x - 2.5)/10)], {x, 0 + a, 10 - a}] == 0.95, {a, .5}] {a -> 0.125}

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Solve[{Integrate[ SquareWave[{2/10, 0}, ((x - 25/10)/10)], {x, a, 10 - a}, Assumptions -> 0 < a < 1] == 95/100, 0 <= a <= 1}, a, Reals] (* {{a -> 1/8}} *)

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There was a really silly mistake. I'm embarrassed for even asking now... z = r cos[theta] was missing from the integral. It's all good now. Thanks for the help anyways! Love you guys :]

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Using Mathematica's region functionality, you can get the centroid like this: cyl=Cylinder[{{0, 0, 0}, {0, 0, 1}}, 1]; RegionCentroid[cyl]; (* {0, 0, 1/2} *) Please have a look at the Wolfram-documentation for further details: RegionCentroid Cylinder Howto calculate the center of gravity yourself Since a cylinder is symmetrical around the center ...

1

Outline As you didn't provide boundary and initial conditions and the function pa'[t] this solution must be generic. Your equation for p[u,t] is linear (I guess pa'(t) means D[p[u,t],u]/.u->a) and can therefore be solved by standard mathematical methods once you provide the boundary and initial conditions. Physically it describes diffusion in a cylinder. A ...

0

I noticed one mistake: your second definition had $K_{n-1}(x)dy$ in the integrand, not $K_{n-1}(y)dy$. Here is the corrected definition: Kin[x_?NumericQ, 0] := NIntegrate[Exp[-Sqrt[τ^2 + x^2]]/Sqrt[τ^2 + x^2], {τ, 0, ∞}] Kin[x_?NumericQ, n_] := NIntegrate[Kin[y, n - 1], {y, x, ∞}] Kin[1, 0] (* 0.421024 *) Kin[1, 1] (* 0.328286 *) Note the use of ...

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