Let L(x) = int(1/t, t=1..x) for all x>0.
a) Find L(1).
b) Find L'(x) and L'(1).
c) Use the Trapezoidal Rule to approximate the value of x (to three decimal places) for which L(x) = 1.
d) Prove that L(x1 * x2) = L(x1) + L(x2), for x1 > 0 and x2 > 0.
[Obs: My CAS is Maple]
Please see the attachment.
Actually, we know that the antiderivative of 1/t is ln t. That is, (ln t)' = 1/t.
So if we do not use any approximation rules ...
This provides an example of using trapezoidal rule.