Question

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

x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16

Numerical answers expected

Answer 1

4(3-1) + 8(4-3) + 6(6-4) + 10(7-6) + 10(9-7) + 12(10-9)

Answer 2

10(7-6) + 10(9-7)
could have been replaced by 10(9-6)
because the height of 10 is the same for both rectangles

Answer 3

Not sure what your definition of "left rectangles" is
You are given 7 points, (1,4), (3,8), ....
So does the height of (1,4) represent the height of the first rectangle?
and (3,8) as the height of the 2nd rectangle?
Also notice that the width of the rectangles is not always the same

You would have to make a nice sketch, and label all the heights and widths.
The rest would simply be the sum of a bunch of "base x heights" calculations.

Answer 4

Looks like Damon had the same interpretation.

Answer 5

I am sorry to tell you but I am confused. I have talked to my friends and everyone has different answers except 2 of them.

Answer 6

81

Answer 7

Using Reiny's steps and Damon's calculation, you would get 70, which is also the right answer.