2015-11-11-113624.sagews

def trapets(f, a, b, n):
    h = (b - a) / n
    return h / 2 * (f(x=a) +
                    2 * sum([f(x=a + i * h) for i in range(1, n)]) +
                    f(x=b))

def simpson(f, a, b, n):
    h = (b - a) / n
    return h / 3 * (f(x=a) +
                    2 * sum([(i % 2 + 1) * f(x=a + i * h) for i in range(1, n)]) +
                    f(x=b))

def TvsS(f, a, b, ns):
    print("{} \t{} \t{} \t{}".format("n", "trapets", "simpson", "integrate"))
    accurate = integrate(f, (x, a, b))
    for n in ns:
        print("{} \t{} \t{} \t{}".format(n, float(trapets(f, a, b, n)), float(simpson(f, a, b, n)), float(accurate)))

#TvsS(1-x^2, 0, 1, [2, 4, 16, 256])
#TvsS(sqrt(1+x^2), 0, 1, [2, 4, 16, 256])

print(simpson(2*x^2+2, 0, 5, 4))

280/3