(906, #23) If your calculator or CAS evaluates integrals numerically, evaluate the integral

where C : x = ln(t), y = e^-t, t = 1..2. Otherwise use the Midpoint Rule with n = 4 to approximate the integral.

Solution: We have

Let f(t) be the integrand. We have to compute :

We use Maple's middlesum( ) command to compute this.

f := t-> ln(t)*exp(-t)*sqrt(t^(-2)+exp(-2*t)):
with(student):
middlesum(f(t),t=1..2);
.05336234855

It shows that M₄ =0.053. (By default, four intervals are used in middlesum( ). )

by C.A.H.