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Expert-verified Found in: Page 777 ### Calculus

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 $9.$

See the step by step solution

## Step 1. Given information

We are given with a function f and its graph.

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

## Step 2. Calculation

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.

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

Thus, the rough value for the average is $9.$ ### Want to see more solutions like these? 