Closed owenbiesel closed 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).
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.