Chapter 11.4, Problem 20E

Solution

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

The numerical integral of $f\left(x\right)={\sec }^{2}x-{\tan }^{2}x$ over the specified interval $\left[0,10\right]$ is $10$ .

Given information: The given function is $f\left(x\right)={\sec }^{2}x-{\tan }^{2}x$ and the specified interval is $\left[0,10\right]$ .

Calculation:

To find the numerical integral of the function $f\left(x\right)={\sec }^{2}x-{\tan }^{2}x$ , 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 ${\left(\frac{1}{\cos x}\right)}^2-{\tan }^{2}x$ , variable $x$ , the lower limit $0$ and the upper limit $10$ .

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

  

Figure (1)

Thus, the numerical integral of the given function is $10$ .