math_231_problem_x.py

def reimann_l(f, a, b, n):
    dx = (b - a)/n
    area = dx * sum(f(a + i*dx) for i in range(n))
    return area

def reimann_r(f, a, b, n):
    dx = (b - a)/n
    area = dx * sum(f(a + i*dx) for i in range(1, n+1))
    return area

def H(x): return 1/x

n = 2
a = reimann_l(H, 1, 2.7, n)
while a > 1:
    n += 1
    a = reimann_l(H, 1, 2.7, n)
print(f"Integral of H from 1 to 2.7 is overestimated to be {a} with {n} subdivisions")

n = 2
a = reimann_r(H, 1, 2.8, n)
while a < 1:
    n += 1
    a = reimann_r(H, 1, 2.8, n)
print(f"Integral of H from 1 to 2.8 is underestimated to be {a} with {n} subdivisions")