Question

Approximate the same area as earlier but this time with eight rectangles is this over approximation or under approximation of the exact area under the graph

Short answer

The area in between the function and x-axis is$20.5sq.units$. this is an under approximation to the original area as the rectangle does not cover every portion between the function and x axis

Step-by-step solution

Given information

We are given a function$f\left(x\right)=x^2$

using the rectangle find the area

We have,

Also

Hence the total area can be given as

$0.5+3+1.5+6+1+5+3+0.5=20.5sq.units$

Also this is an under approximation to the original area as the rectangle does not cover every portion between the function and x axis.