# What is the problem with that integral ?

I try to integrate this:

sage: integrate(integrate(integrate(2*cos(z)*sin(atan((2*cos(y)-0.5+x)/(2*sin(y)))),y,0,pi/2),x,0,1),z,0,pi/2);


There is a problem :

"ECL says: In function ZEROP, the value of the only argument is
((RAT SIMP) -0.5 1.0)
which is not of the expected type NUMBER"


Could you help me please ?

Wolfram does it so I think it is not an error of the function maybe a limit ?

It works with python:

def f1(y,x,z): ...     return  2*np.cos(z)*np.sin(np.arctan((2*np.cos(y)-0.5+x)/(2*np.sin(y))))


...

tplquad(f1,0,np.pi/2, lambda z: 0, lambda z:1, lambda z, x: 0, lambda z, x: np.pi/2) (1.9792263101075036, 2.1973826204252407e-14)

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1

The first integral doesnt work, so the others two integrals neither.

1

It seems that the inner integral doesnt converge. Try to do only the inner integral in any CAS (including mathematica).

With python "tplquad" it works. I don't have mathematica. The inner integral works with python. It works with Wolfram.

2

I think that the problem here is that each integral is evaluated without taking in account the constraints of the other integrals, so it is possible that the inner integral diverges depending in the values of $x$ and $z$. If this is true then putting some constraints before to the integral on $x$ and $z$ probably help in this problem.