Q 21. - 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].

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

Step-by-Step Solution

Answer

Area is equal to 1.219

Step 1.Given information

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

Step 2. Explanation

Consider the function $f\left(x\right)=\sqrt{x-1},\left[a,b\right]=\left[2,3\right]$

Area $={\int }_2^3\sqrt{x-1}$

          $$\begin{gathered} ={\left[\frac{{(x-1)}^{{\displaystyle \frac{1}{2}}+1}}{{\displaystyle \frac{1}{2}}+1}\right]}_2^3 \\ =1.219 \end{gathered}$$