Victoria V. answered • 06/30/18

20+ years teaching basic Calculus & beyond.

The actual integral evaluates to (x^4)/4 from 0 to 3 = 20.25.

Graph f(x)=x-cubed.

If the rectangles are INSCRIBED, I think that means they are fully under the curve, with the left vertical edge of each rectangle touching the graph of x-cubed.

Each rectangle is 1 unit wide.

The rectangle from 0 to 1 has an area of 0

[f(0) = 0, so Area = lw = (0)(1) = 0]

The rectangle from 1 to 2 has an area of 1

[f(1) = 1, so Area = lw = (1)(1) = 1]

The rectangle from 2 to 3 has an area of 8

[f(2) = 8, so Area = lw = (8)(1) = 8]

So the estimated area is the sum of these three rectangles, so it is

0 + 1 + 8 = 9

The error is 9 - 20.25 = -11.25, an UNDERestimate (all of the rectangles lie below the graph, so do not contain all of the area under the x-cubed curve.)

The abs val of the error is 11.25