numerical_integral( function , begin , end [ , params=[] ] )

The numerical integral in SageMath of function from begin to end. The returned output is a tuple consisting of the value of the integral and and an error estimate.

This operation assumes that the variable of integration is the first argument of function. The optional params argument is used to include additional numerical parameters as a list. These parameters are assigned in the order in which they appear as arguments in the definition of function.

The function to be integrated must return real values, not complex values.

For complicated integrals SciPy’s quad is significantly faster. It needs to be imported from scipy.integrate. The argument corresponding to params is named args and works the same way.

Examples:

numerical_integral( x, 0, 1 )

f(x,a,b) = x + a + b^2
[numerical_integral( f, 0, 1, params=[n,0] ) for n in range(1,4)]

f(x,a,b) = x + a + b^2
[numerical_integral( f, 0, 1, params=[0,n] ) for n in range(1,4)]

Related operations:   integral

Operation category: calculus operations sagemath-docs