Question

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

Answer 1

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

The definite integral

`int_0^1 f(x) dx`

can be approximated by Trapezoid Rule

`approx T_6=[f(0/6)+2f(1/6)+2f(2/6)+2f(3/6)+2f(4/6)+2f(5/6)+f(6/6)]{1-0}/{2(6)}approx 0.54`