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So we have :enter image description here

 (1/3)*sig0*h^3*(int(int(sin((1/3)*arctan(y, x)), x = 0 .. r), y = 0 .. 2*Pi)) 

Is it possible to optimise it? (in maple or any other way...)

How I got here:

> R := 1;  H := h; sigma[0] := sig0;  sigma := sigma[0]*z^2*sin((1/3)*`ϕ`);  toCar := eval(sigma, {r = sqrt(x^2+y^2), z = z, `ϕ` = arctan(y, x)});  > Q := int(int(int(toCar, x = 0 .. r), y = 0 .. 2*Pi), z = 0 .. H); 
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    Could you be more concrete? Concerning which variables do you want to optimize it. Do you want to minimize or maximize it, are there any constraints?2011-05-18

1 Answers 1

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By optimize, I assume you are meaning simplify. I don't see a parameter to optimize over. The limits on the integrals look like the differentials should be $\rho \; d\rho \; d\theta$, not $dx \; dy$. If so, you have $\int_0^{2\pi}\int_0^r\sin(\frac{\theta}{3})\rho \; d\rho \; d\theta=-3\frac{r^2}{2}\cos(\frac{\theta}{3})\mid_0^{2\pi}=\frac{9r^2}{4}$

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    Looks good to me2011-05-18