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Trapezoidal rule

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]

Solution Preview

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 ...

Solution Summary

This provides an example of using trapezoidal rule.