   Chapter 4.3, Problem 30E

Chapter
Section
Textbook Problem

Evaluating a Definite Integral Using a Geometric Formula In Exercises 23-32, sketch the region whose area is given by the definite integral. Then use a geometric formula to evaluate the integral ( a > 0 , r > 0 ) . ∫ − a a ( a − | x | )   d x

To determine

To Graph: The integral aa(a|x|)dx.

Explanation

Given: aa(a|x|)dx

Graph: Consider the provided integral aa(a|x|)dx. Sketch the graph of the function f(x)=a|x|.

To find the graph for the region, replace x=a,x=0 and x=a. Therefore,

At x=a,

f(x)=a|x|f(a)=a|a|=aa=0

To determine

To calculate: Value of the integral aa(a|x|)dx using geometric formula.

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