Q 25. - 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].

$f\left(x\right)={\left(x-2\right)}^2+1,\left[a,b\right]=\left[1,3\right]$

Step-by-Step Solution

Answer

Answer is $\frac{8}{3}$

Step 1. Given information

Function is $f\left(x\right)={\left(x-2\right)}^2+1,\left[a,b\right]=\left[1,3\right]$

Step 2. Explanation

Consider the function

Area $={\int }_1^3{\left(x-2\right)}^2+1 dx$

           $$\begin{gathered} ={\left[\frac{{(x-2)}^3}{3}+x\right]}_1^3 \\ =\frac{8}{3} \end{gathered}$$