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Q. 15

Expert-verifiedFound in: Page 777

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

The solution is $9.$

We are given with a function f and its graph.

The objective is to estimate the area of f on [-4,4].

Consider the rough approximation for the function given in the diagram.

The values of the functions are at $f\left(0\right)=54andf\left(3\right)=0$

Then, the rough value for the average can be calculated as shown below.

$=\frac{1}{4-(-4)}{\int}_{-4}^{4}(54-18x)dx\phantom{\rule{0ex}{0ex}}=\frac{1}{8}{[54x-9{x}^{2}]}_{-4}^{4}=\frac{1}{8}[216-144+216+144]\phantom{\rule{0ex}{0ex}}=\frac{1}{8}\left(432\right)\phantom{\rule{0ex}{0ex}}=9$

Thus, the rough value for the average is $9.$

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