Question

How do you find Find the Riemann sum that approximates the integral `int_0^9sqrt(1+x^2)dx` using left endpoints with `n=6`?

Answer 1

Let `f(x)=sqrt{1+x^2}`.

`Delta x={b-a}/n={9-0}/6=1.5`

`L_6=[f(x_0)+f(x_1)+cdots+f(x_5)]cdot Delta x`

`=[f(0)+f(1.5)+f(3)+f(4.5)+f(6)+f(7.5)]cdot(1.5)`

`approx 34.84`