5.4E: Average Value of a Function Exercises
- Page ID
- 13817
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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) \(\displaystyle f(x)=x^5,a=−1,b=1\)
- Answer:
- \(\displaystyle f_{ave}=0\)
112) \(\displaystyle f(x)=\sqrt{4−x^2},a=0,b=2\)
113) \(\displaystyle f(x)=(3−|x|),a=−3,b=3\)
- Answer:
- \(\displaystyle \frac{3}{2}\)
114) \(\displaystyle f(x)=sinx,a=0,b=2π\)
115) \(\displaystyle f(x)=cosx,a=0,b=2π\)
- Answer:
- \(\displaystyle f_{ave}=0\)
J5.4.1) \(\displaystyle f(x)=\sqrt[3]{x},a=1,b=8\)
- Answer:
- \(\displaystyle f_{ave}= \frac{45}{28}\)
J5.4.2) \(\displaystyle f(x)=\frac{1}{x},a=2,b=5\)
- Answer:
- \(\displaystyle f_{ave}= \frac{1}{3}ln(2.5)\)