Hello people!
I've been trying to solve this integral:
sage: integrate(sqrt(sec(x)-1),x,pi/2,pi)
integrate(sqrt(sec(x) - 1), x, 1/2*pi, pi)
Since sage failed to produce a symbolic result, I tried with
numerical_integral
sage: numerical_integral(sqrt(sec(x)-1),pi/2,pi)
(nan, nan)
But that failed also... So I tried with mathematica:
sage: mathematica_console()
Mathematica 7.0 for Linux x86 (32-bit)
Copyright 1988-2008 Wolfram Research, Inc.
In[1]:= Integrate[Sqrt[Sec[x]-1],{x,Pi/2,Pi}]
Out[1]= I Pi
So mathematica says it's a pure imaginary number, which I know to be true.
I know that symbolic integration is quite complicated to develop, but
numerical integration should be fairly easy to extend to complex
numbers. Am I missing something? Why does numerical_integral return NaN?
Perhaps i'ts not because of the complex result, in which case how could
I solve the integral without recurring to mathematica?
thanks!
Oscar.
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