Question

How do you calculate the right hand and left hand riemann sum using 4 sub intervals of `f(x)= 3x` on the interval [1,5]?

Answer 1

See the explanation section, below.

Explanation:

`f(x) = 3x` `[a,b] = [1,5]` and `n=4`

Assuming that we are using subintervals of equal length, we get:

`Deltax = (b-a)/n = (5-1)/4 = 1`

Endpoints of the subintervals are found by starting at `a` and successively adding `Delta x` until we reach `b`

The endpoints are `1,2,3,4,5`

(The subintervals are: `[1,2], [2,3], [3,4], [4,5]`

The left endpoints are `1,2,3,4`

`L_4 = f(1)Deltax + f(2)Deltax + f(3)Deltax + f(4)Deltax`

(Do the arithmetic.)

The right endpoints are `2, 3, 4, 5`

`R_4 = f(2)Deltax + f(3)Deltax + f(4)Deltax + f(5)Deltax`

(Do the arithmetic.)