Question

Let `f(x) = x^2` and how do you compute the Riemann sum of f over the interval [6,8], using the following number of subintervals (n=5) and using the right endpoints?

Answer 1

See the explanation section, below.

Explanation:

`f(x) = x^2`

`[a,b] = [6,8]`

and `n=5`.

Find `Delta x = (b-a)/n = 2/5` (or `= 0.4` if you prefer decimals).

Find the intervals.

Start at `a` and successively add `Delta x` until you get to `b`.

`[6,6 2/5], [6 2/5, 6 4/5], [6 4/5, 7 1/5], [7 1/5, 7 3/5], [7 3/5, 8]`

(or `[6,6.4], [6.4, 6.8], [6.8, 7.2], [7.2, 7.6], [7.6, 8]` using decimals)

The right endpoints are: `x_1=6 2/5, x_2=6 4/5, x_3=7 1/5, x_4=7 3/5, x_5=8`

(or `x_1=6.4, x_2=6.8, x_3=7.2, x_4=7.6, x_5=8` using decimals)

Now use the right Riemann sum for `n=5`

`R_5 = f(x_1)Deltax + f(x_2)Deltax + f(x_3)Deltax + f(x_4)Deltax + f(x_5)Deltax"`

Now, do the arithmetic.