As it is well known the integral of 1/(cos(theta)^2) is tan(theta)
But there seems to be a problem evaluating the definite integral:
var("theta", domain="real")
> (1/cos(theta)^2).integral(theta, -pi/4 , pi/4 , algorithm='sympy') #
> Works
> (1/cos(theta)^2).integral(theta, -pi/4 , pi/4 , algorithm='fricas') #
> Works
> (1/cos(theta)^2).integral(theta, -pi/4 , pi/4 , algorithm='giac') #
> Works
> (1/cos(theta)^2).integral(theta, -pi/4 , pi/4 , algorithm='maxima') #
> Says "Integral is divergent." [image: spin-eye]
Are you sure the choice of Maxima as the default backed is the correct one?
By the way Maxima has no problem calculating the indefinite integral:
> (1/cos(theta)^2).integrate(theta, algorithm='maxima')
And as you guys know there is no asymptote or anything weird in the
integrand between -pi/4 to pi/4 so I don't know what the difficulty is in
calculating this area:
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