Question

Help with approximation question.

Answer 1

can you answer helping

Answer 2

yeah. i know n= 4 and dividing that by b-a gives 1

Answer 3

so (b-a)/4 = 1 correct?

Answer 4

@helping

Answer 5

Plot it, then divided the interval into four equal lengths, then draw rectangles from the lowest point of each interval and then back from the highest point of each interval, so you have two rectangles on each interval, one over-estimating the area and the other under-estimating it.

Answer 6

I used geogebra to make the attached plot. (Free and not difficult to use.) You can guess that the curve cuts the x-axis at x=2 and x=6, then verify this by finding the roots (or solutions) of the given function taken as a quadratic. 6-2=4, as you've said, so the four equal intervals are 1 unit long. Now evaluate f(x) at 3, 4 and 5 to obtain the heights of the required rectangles. The green rectangles in the attached plot overestimate the area under the curve and are partially hidden by the red rectangles that underestimate the area.