Chapter 6.4, Problem 73AYU

To determine

To find: The average rate of change of $f$ from $0$ to $\frac{\pi }{2}$ .

Answer to Problem 73AYU

Solution:

Average rate of change $=$ $\frac{2}{\pi }$

Explanation of Solution

Given:

  $f\left(x\right)=\sin x$

Formula used:

Average rate of change $=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

Calculation:

  $f\left(x\right)=\sin x$

  $f\left(b\right)=f\left(\frac{\pi }{2}\right)=\sin \frac{\pi }{2}=1$

  $f\left(a\right)=f\left(0\right)=\sin 0=0$

Average rate of change $=\frac{f\left(b\right)-f\left(a\right)}{b-a}=\frac{1-0}{\frac{\pi }{2}-0}=\frac{2}{\pi }$