Chapter 6, Problem 38RE

(a)

To determine

To find average value of function.

Answer to Problem 38RE

Average value of $y=\sqrt{x}$ over interval $\left[0,4\right]$ is $1/2$ .

Explanation of Solution

Given:Function is

  $y=\sqrt{x}$

Formula used:

Average value of a function over an interval $\left[a,b\right]$ is given by

Average value $=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

Calculation: Average value of $y=\sqrt{x}$ over interval $\left[0,4\right]$ is

  $\begin{array}{l}\text{Average value}=\frac{\left(\sqrt{4}-\sqrt{0}\right)}{4-0}\\ =\frac{2}{4}\\ =\frac{1}{2}\end{array}$

(b)

To determine

To find average value of function.

Answer to Problem 38RE

Average value of $y=a\sqrt{x}$ over interval $\left[0,a\right]$ is $\sqrt{a}$ .

Explanation of Solution

Given: Function is

  $y=a\sqrt{x}$

Formula used:

Average value of a function over an interval $\left[a,b\right]$ is given by

Average value $=\frac{f\left(b\right)-f\left(a\right)}{b-a}$

Calculation:Average value of $y=a\sqrt{x}$ over interval $\left[0,a\right]$ is

  $\begin{array}{l}\text{Average value}=\frac{\left(a\sqrt{a}-a\sqrt{0}\right)}{a-0}\\ =\frac{a\sqrt{a}}{a}\\ =\sqrt{a}\end{array}$