Question

Using Right Riemann Sums, approximate the area under the curve `5x^2-4x` in the interval `[0,3]` with `6` strips?

Answer 1

`35.875`

Explanation:

We have:

`f(x) = 5x^2-4x`

We want to calculate over the interval `[0,3]` with `6` strips; thus:

`Deltax = (3-0)/6 = 0.5`

Note that we have a fixed interval (strictly speaking a Riemann sum can have a varying sized partition width). The values of the function are tabulated as follows;

Right Riemann Sum

`R RS = sum_(r=1)^6 f(x_i)Deltax_i`
`" " = 0.5 * (-0.75 + 1 + 5.25 + 12 + 21.25 + 33)`
`" " = 0.5 * (71.75)`
`" " = 35.875`

Actual Value

For comparison of accuracy:

`Area = int_0^3 \ 5x^2-4x \dx`
`" " = [(5x^3)/3-2x]_0^3`
`" " = 45-6`
`" " = 39`