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?

Steve today at 10:43pm
the area is

6
∑ f(xk) ∆xk
k=1

where the xk are 3,4,6,7,9,10
and the ∆xk are 2,1,2,1,2,1

so just add 'em up.


I don’t understand what Steve is explaining

Answer 1

the problem involves a Riemann sum. Apparently you have not yet been introduced to summation notation. Since you are to use right-rectangles, you evaluate f(x) at the right side of each interval. The intervals need not be of equal widths, so there is no need for trying to take values at half-way points. So, the sum is

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

f(3)*(3-1) + f(4)*(4-3) + f(6)*(6-4) + f(7)*(7-6) + f(9)*(9-7) + f(10)*(10-9)
= 8*2 + 6*1 + 10*2 + 10*1 + 12*2 + 16*1
= 92

Answer 2

81