Question

Suppose `f(x)= 2x^(2)-1`, how do you compute the Riemann sum for f(x) on the interval [-1,5] with partition {-1,2,4,5} using the left-hand endpoints as sample points?

Answer 1

See below.

Explanation:

The left endpoints are `-1`, `2`, and `4`.

The various `Deltax`'s are

`Deltax_1 = 2-(-1) = 3`, `Deltax_2 = 4-(2) = 2`, `Deltax_3 = 5-(4) = 1`

The sum we seek is

`f(-1)Deltax_1 + f(2)Deltax_2+f(4)Deltax_3 = (1)(3)+(7)(2)+(31)(1) = 48`