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5

Since your integrand does not approach zero but a finite positive number, Limit[Exp[-16.136 (1 - Exp[-0.012*t])], t -> Infinity] (* 9.82255*10^-8 *) the integral over {t, 0, Infinity} does not converge. By the way, the error in the NIntegrate[integrand, {t, 0, 1000}] should be about 10^-7, which seems better than R. In fact, the precision seems ...


4

Both Module and DynamicModule are shadowing the global variables x and y in the example in which you use them. The demonstration is best written without using either Module or DynamicModule. Manipulate[ ContourPlot[f, {x, -1, 1}, {y, -1, 1}, Contours -> 20, Epilog -> Dynamic[Arrow[{pt, pt + grad /. {x -> pt[[1]], y -> pt[[2]]}}]]], {f, ...


4

When you try to NIntegrate your expression, the error messages include: "suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small". Your expression does not have a singularity, its integral is manifestly not zero, it is not oscillatory, so it must be a numerical precision problem. ...


4

The brute force method to arrive at your second solution f[z_] = 1/beta/(2*z)/(1 - beta); cl = CoefficientList[f[z], 1/z]; cl.Integrate[(1/z)^Range[0, Length[cl] - 1], z] Log[z]/(2*(1 - beta)*beta)


3

Perhaps what you are looking for is: A = {{2, -1, 0}, {-1, 2, -1}, {0, -1, 1}}; Integrate[Exp[(-x . A . x)/2], x ∈ FullRegion[3]] 2 Sqrt[2] π^(3/2)


1

You could use a definite integral: Integrate[1/beta/(2*z0)/(1 - beta), {z0, 1, z}, Assumptions -> {z > 1, 0 < beta < 1}] (* Log[z]/(2 beta - 2 beta^2) *) Of course, this requires by-hand tuning of the lower limit, but if you want a certain form (i.e. a certain choice of offset), then that's required anyway.


1

This is taking your first modification of the original code and just changing the way f is defined, then using that function inside the module. It seems to work fine for me. Clear[x, y, f]; x = 10;(*Global values have no effect on Module...*) y = 12;(*Global values have no effect on Module...*) f[x_, y_] := E^(-x^2 - y^2) + x y; Manipulate[ Module[ {x, ...



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