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:

Step-by-step 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.

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