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8 August, 13:19

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:

+5
Answers (2)
  1. 8 August, 16:23
    +1
    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
  2. 8 August, 16:39
    +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.
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