Q. 5 - Calculus

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

Step-by-Step Solution

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 1: Given information

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

Step 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.