Chapter 11.4, Problem 12E

Solution

To calculate: The numerical integral of the function $f\left(x\right)=x^2$ by graphing calculator over the specified interval.

The numerical integral of $f\left(x\right)=x^2$ over the specified interval $\left[-4,0\right]$ is $\frac{64}{3}$ .

Given information: The given function is $f\left(x\right)=x^2$ and the specified interval is $\left[-4,0\right]$ .

Calculation:

To find the numerical integral of the function $f\left(x\right)=x^2$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{MATH}}$ key and select $\text{fnInt(}$ under math. Enter the given function $x^2$ , variable $x$ , the lower limit $-4$ and the upper limit $0$ .

Press the $\boxed{\text{ENTER}}$ key to find the numerical integral of the function and convert it to fraction as shown below in figure (1).

  

Figure (1)

Thus, the numerical integral of the given function is $\frac{64}{3}$ .