Question

How do you estimate the area under the graph of `f(x)=4sqrt(x)` from `x=0` to `x=4` using four approximating rectangles and right endpoints?

Answer 1

Find the value of `f(x)` for each integer value: `0, 1, 2, 3, 4`
giving 4 sub-ranges:
`[f(0),f(1)`] `= [0,2.0`],
`[f(1),f(2)`] `= [2.0, 5.6`] (approx.)
`[f(2),f(3)`] `= [5.6, 6.8`] (approx.)
`[f(3),f(4)`] `= [6.8, 8.0`]

Use the mid point of each range as the rectangular height for the `4` rectangles (note: the width of each rectangle is 1)

Approximate area
`= 1.0 + 3.8 + 6.2 + 7.4`
`= 18.4`