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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? – Listing May 18 '11 at 17:14
up vote 1 down vote accepted

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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thank you so wary much!) – Kabumbus May 18 '11 at 17:31
so I will get $ 3/4 * r^2 * h^3 * sig0 $ ? – Kabumbus May 18 '11 at 17:59
Looks good to me – Ross Millikan May 18 '11 at 18:01

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