Q 22. - Calculus

Question

Your calculator should be able to approximate the area between a graph and the x-axis. Determine how to do this on your particular calculator, and then, in Exercise, use the method to approximate the signed area between the graph of each function f and the x-axis on the given interval [a, b].

$f\left(x\right)=x^2,\left[a,b\right]=\left[0,3\right]$

Step-by-Step Solution

Answer

Answer is 9

Step 1. Given information

$f\left(x\right)=x^2,\left[a,b\right]=\left[0,3\right]$

Step 2. Explanation

Consider the function $f\left(x\right)=x^2$

Area $={\int }_0^3{x}^2$

          $$\begin{gathered} ={\left[\frac{x^3}{3}\right]}_0^3 \\ =9 \end{gathered}$$