Question

How do you Find the Riemann sum for `f(x)=x^3` on the interval `[0,5]` using right endpoints with `n=8`?

Answer 1

Let us find `Delta x`.

`Delta x={b-a}/n={5-0}/8=5/8`

Now, we can find the right sum `R_8`.

`R_8=[f(5/8)+f(10/8)+f(15/8)+f(20/8)+f(25/8)+f(30/8)+f(35/8)+f(40/8)]cdot Delta x`

`=[(5/8)^3+(10/8)^3+(15/8)^3+(20/8)^3+(25/8)^3+(30/8)^3+(35/8)^3+(40/8)^3]cdot 5/8`

`approx 197.75`