Question

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

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

Numerical Answers Expected!
Answer for Blank 1:

Answer 1

Explanation:

Given is a table of x, f(x) as below

x 1 3 4 6 7 9 10

f(x) 4 8 6 10 10 12 16

Mid pt 6 7 8 10 11 14

width of

interval 2 1 2 1 2 1

dA1 12 7 16 10 22 14

area = area of all rectangles= 81 sq units.

Answer 2

Divide the area into 6 portions and find the sum of each one to find the value of the final integral:

f(x)dx = 2(8+4)/2 + 1 (8+6)/2 + 2 (6+10)/2 + 1(10+10)/2 + 2 (10+12)/2 + 1 (12+16)/2

= 12 + 7 + 16 + 10 + 22 + 14 = 81 sq units