On 2/23/11 11:14 PM, Ronald L. Rivest wrote:
Let f(x,y) be a function such that
integral(f(x,y),y,0,x)
doesn't evaluate to anything simpler, such as
f(x,y) = (y+1) ^ (y+1) ^ x
How can I then compute the (definite) integral of f over the region
0<= y<= x<= 1
I want a numeric integration, but
numerical_integral(numerical_integral(f,0,x),0,1)
doesn't work, since f takes two parameters, not one. And
numerical_integral(integral(f(x,y),y,0,x),0,1)
doesn't work either, since the inner integral doesn't evaluate.
I couldn't find guidance on this in the documentation or elsewhere...
(Please let me know if this request should be posted elsewhere instead
of here...)
You might try using scipy to do this numerical integral. See
http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.dblquad.html#scipy.integrate.dblquad
for documentation of the function. Here is your example, I think:
sage: f(y,x) = (y+1) ^ (y+1) ^ x
sage: from scipy.integrate import dblquad
sage: dblquad(f,0,1,lambda x: 0, lambda x: x)
(0.76066264344246226, 8.4450518072205739e-15)
This matches up with Mathematica:
NIntegrate[f[x, y], {x, 0, 1}, {y, 0, x}] gives 0.760663
Note that for scipy, the function must take two arguments, the first
being the *y* value, and the second being the x value.
Thanks,
Jason
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