Question

Given the table below for selected values of f(x), use 6 right rectangles to estimate the value of the integral from 1 to 10 of f(x)dx.

Table:
1 3 4 6 7 9 10
4 8 6 10 10 12 16

The only problem I'm having with this is figuring out the values of f(2.5), f(5.5), and f(8.5) since each rectangle should be 1.5 units apart. Is there a way to solve this without those values?

Answer 1

the area is

6
∑ f(x_{_k}) ∆x_{_k}
k=1

where the x_{_k} are 3,4,6,7,9,10
and the ∆x_{_k} are 2,1,2,1,2,1

so just add 'em up.