Regarding numerical approximation of
, where
is a piecewise defined
function, Sage can
sage: f1 = x^2 sage: f2 = 5-x^2 sage: f = Piecewise([[(0,1),f1],[(1,2),f2]]) sage: f.trapezoid(4) Piecewise defined function with 4 parts, [[(0, 1/2), x/2], [(1/2, 1), 9*(x - 1/2)/2 + 1/4], [(1, 3/2), (x - 1)/2 + 5/2], [(3/2, 2), 11/4 - 7*(x - 3/2)/2]] sage: f.riemann_sum_integral_approximation(6,mode="right") 19/6 sage: f.integral() 3
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