Question

How do you use n = 5 equally divided subdivisions to estimate the integral from 1 to 3 of `(1/x^2)dx` with the right-hand Riemann sum?

Answer 1

See the explanation.

Explanation:

`f(x) = 1/x^2`

The interval `[a,b]` is `[1,3]` and `n = 5`

So `Delta x = (b-a)/n = (3-1)/5 = 2/5`

The subintervals are:

`[1, 7/5]`, `[7/5, 9/5]`, `[9/5, 11/5]`, `[11/5, 13/5]`, `[13/5, 3]`

The right endpoints are:

`7/5, 9/5, 11/5, 13/5, 3`

Find `f` of each right endpoint times `2/5` (because `Delta x = 2/5` is the base of each rectangle.) and then add.
(Or find `f` of each right endpoint, add those and then multiply by `2/5`)

`f(7/5)*2/5+ f(9/5)*2/5 + f(11/5)*2/5 + f(13/5)*2/5+f(3)*2/5`

(or `(f(7/5)+ f(9/5) + f(11/5) + f(13/5)+f(3))*2/5`