Question

How do you Use Simpson's rule with `n=6` to approximate the integral `int_0^1e^-sqrt(x)dx`?

Answer 1

Let `f(x)=e^{-sqrt{x}}`.

By Simpson's Rule,

#S_6=[f(0/6)+4f(1/6)+2f(2/6)+4f(3/6)+2f(4/5)+4f(5/6)+f(6/6)]{Delta x}/3 approx 0.534#,

where `Delta x={b-a}/n={1-0}/6=1/6`