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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

For each shaded region in Problems 7-12, (a) find the points of intersection of the curves, (b) form the integral that represents the area of the shaded region, and (c) find the area of the shaded region.

Chapter 13.3, Problem 12E, For each shaded region in Problems 7-12, (a) find the points of intersection of the curves, (b) form

(a)

To determine

To calculate: The point of intersection of the curve

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.3, Problem 12E , additional homework tip  1

Explanation

Given information:

The provided region is:

Formula used:

The steps for calculating the point of intersection of the curve are:

Step 1: Consider the equations in the curve.

Step 2: Solve the equations for any variable

Step 3: Substitute the value of the variable in any of the equation to calculate the value of other variable.

Calculation:

Consider the curve:

Consider the formula:

The equations are:

y=xx2

And

y=x3x2

Substitute x3x2 for y in first equation to get:

x3x2=xx2

Solve to get:

x3x2x+x2=0x3x=0x(x21)=0x(x1)(x+1)=0

Thus,

x=0 or x=

(b)

To determine

To calculate: The integral that represents the area of the shaded region.

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.3, Problem 12E , additional homework tip  2

(c)

To determine

To calculate: The area of the region

Mathematical Applications for the Management, Life, and Social Sciences, Chapter 13.3, Problem 12E , additional homework tip  3

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