   Chapter 8.1, Problem 84E

Chapter
Section
Textbook Problem

AreaThe graphs of f ( x ) = x and g ( x ) = a x 2 intersect at the points ( 0 , 0 ) and ( 1 / a , 1 / a ) . Find a ( a > 0 ) such that the area of the region bounded by the graphs of these two functions is 2 3 .

To determine

To calculate: The constant a.

Explanation

Given:

f(x)=x , g(x)=ax2 and area A=23

Calculation:

Consider the following functions,

f(x)=x and g(x)=ax2

Draw the graph of two functions,

Therefore, point of Intersection of these functions are

(0,0) and (1a,1a)

Therefore the area is given by:

A=01a(f(x)g(x))dx=01a(x

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