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 | 1 | initial version |
My first thought would be to switch your integral to polar coordinates so you don't need the max bit at all.
sage: r = 1.5
sage: var('rad,theta')
(rad, theta)
sage: var('a')
a
sage: integrate(integrate(a*(r - rad^2)*rad,theta,0, 2*pi),rad,0,sqrt(r))
1.125*pi*a
sage: solve(_==1,a)
[a == 8/9/pi]
sage: n(_[0].rhs())
0.282942121052258
I think I did the change of coordinates right - $r dr d\theta$, right?
Now, this doesn't answer the more general question of how to do this, where I would suggest using find_root - or just using Scipy in general, perhaps, since you are already using it, if you really do not need the symbolic capabilities; the syntax may end up more natural, who knows?
| | 2 | No.2 Revision |
My first thought would be to switch your integral to polar coordinates so you don't need the max bit at all.
sage: r = 1.5
sage: var('rad,theta')
(rad, theta)
sage: var('a')
a
sage: integrate(integrate(a*(r - rad^2)*rad,theta,0, 2*pi),rad,0,sqrt(r))
1.125*pi*a
sage: solve(_==1,a)
[a == 8/9/pi]
sage: n(_[0].rhs())
0.282942121052258
I think I did the change of coordinates right - $r dr d\theta$, right?
Now, this doesn't answer the more general question of how to do this, this with a max and a double numerical integral, where I would suggest using find_root - or just using Scipy in general, perhaps, since you are already using it, if you really do not need the symbolic capabilities; the syntax may end up more natural, who knows?
