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sagemath / sagecell

The Sage Cell Server---providing a way to embed Sage computations into any web page.
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Calculus Error #578

Closed owenbiesel closed 9 months ago

owenbiesel commented 9 months ago

The symbolic calculator seems to be making a mistake while simplifying integrals: the integral

integral(sqrt(x^2+x^4),x,-2,2)

returns 0, even though the function is nonnegative, and positive away from x = 0. I suspect it is attempting to rewrite the integrand as x sqrt(1 + x^2), which is an odd function with integral 0, whereas it should rewrite the integrand as abs(x) sqrt(1+x^2). The numerical integrator correctly returns a value for the integral of about 6.79.

novoselt commented 9 months ago

That has nothing to do with SageMathCell however, which is just sending the code to SageMath! It seems to me that similar issues are popping up regularly over the years and they are due to bugs in the underlying software (most likely not even SageMath).

roed314 commented 9 months ago

I would suggest browsing the issues here to see if you can find one that already addresses this problem, and creating one if you can't.