Question

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

Answer 1

Answer:

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.

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