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# 5.4E: Average Value of a Function Exercises

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## 5.4: The Average Value of a Function Exercises

In the following exercises, find the average value $$\displaystyle f_{ave}$$ of f between a and b, and find a point c, where $$\displaystyle f(c)=f_{ave}$$

110) $$\displaystyle f(x)=x^2,a=−1,b=1$$

111) $$\displaystyle f(x)=x^5,a=−1,b=1$$

$$\displaystyle f_{ave}=0$$

112) $$\displaystyle f(x)=\sqrt{4−x^2},a=0,b=2$$

113) $$\displaystyle f(x)=(3−|x|),a=−3,b=3$$

$$\displaystyle \frac{3}{2}$$

114) $$\displaystyle f(x)=sinx,a=0,b=2π$$

115) $$\displaystyle f(x)=cosx,a=0,b=2π$$

$$\displaystyle f_{ave}=0$$
J5.4.1) $$\displaystyle f(x)=\sqrt[3]{x},a=1,b=8$$
$$\displaystyle f_{ave}= \frac{45}{28}$$
J5.4.2) $$\displaystyle f(x)=\frac{1}{x},a=2,b=5$$
$$\displaystyle f_{ave}= \frac{1}{3}ln(2.5)$$