Q. 21 - Precalculus Enhanced with Graphing Utilities

Question

Use the result obtained in Problem $20$ to find the area enclosed by $f\left(x\right)=-5x^2+8$ the $x-axis$ and the lines $x=-1$ and $x=1$

Step-by-Step Solution

Answer

The area is $12.67$.

Step 1. Given information

It is given that $f\left(x\right)=-5x^2+8$, we need to use the result of the problem $20$ to determine the area enclosed by $f\left(x\right)$, the $x-axis$ and the lines $x=-1$ and $x=1$.

Step 2. Simplify

$f\left(x\right)=-5x^2+8$

For, $x=-1$,

$f(-1)=-5{(-1)}^2+8$

           $=3=y_0$

For $x=0$,

$f\left(0\right)=-5{\left(0\right)}^2+8$

       $=8=y_1$

For $x=1$,

$y=-5{\left(1\right)}^2+8$

   $=3$$=y_2$

The area is,

Area $=\frac{1}{3}(y_0+4y_1+y_2)$

         $=\frac{1}{3}(3+4·8+3)$

          $=\frac{38}{3}$

          $=12.67$

         $=\frac{38}{3}$