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

Question

x: 1 , 3 , 4 , 6 , 7 , 9 , 10

f(x): 4 , 8 , 6 , 10 , 10 , 12 , 16

Answer 1

Left rectangles means you use the left point for the height of the rectangle.

The areas then would be:

A_rectangle = Height•Width

A1 = 4(2) = 8

A2 = 8(1) = 8

A3 = 6(2) = 12

A4 = 10(1) = 10

A5 = 10(2) = 20

A6 = 12(1) = 12

The total area = 8 + 8 + 12 + 10 + 20 + 12 = 70 (this is the estimate for the value of the integral)

Answer 2

∫_{(from 1 to 10)} f(x)dx ≈ f(1)(3-1) + f(3)(4-3) + f(4)(6-4) + f(6)(7-6) + f(7)(9-7) + f(9)(10-9)

= 8 + 8 + 12 + 10 + 20 + 12 = 70