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29 votes
29 votes
Find the average value of the function
f(x) = 4 {x}^(3)on the interval
1 \leqslant x \leqslant 4

User Alex Nikolsky
by
2.9k points

1 Answer

14 votes
14 votes

Given the function f(x) defined as:


f(x)=4x³

The average value on the interval [1, 4] is given by:


\bar{f}=(f(4)-f(1))/(4-1)

Evaluating the function at x = 4 and x = 1:


\begin{gathered} f(4)=4\cdot4³=256 \\ \\ f(1)=4\cdot1³=4 \end{gathered}

Using these values for the average value of f:


\begin{gathered} \bar{f}=(256-4)/(3)=(252)/(3) \\ \\ \therefore\bar{f}=84 \end{gathered}

User Bilbohhh
by
2.3k points