Chapter 8.1, Problem 84E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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)=xÂ ,Â g(x)=ax2Â andÂ areaÂ A=23

Calculation:

Consider the following functions,

f(x)=xÂ andÂ g(x)=ax2

Draw the graph of two functions,

Therefore, point of Intersection of these functions are

(0,0)Â andÂ (1a,1a)

Therefore the area is given by:

A=âˆ«01a(f(x)âˆ’g(x))dx=âˆ«01a(xâˆ’

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