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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding Area with a Double Integral In Exercises 31-36, use a double integral to find the area of the region bounded by the graphs of the equations. See Example 4.

y = 4 x 2 , y = x + 2

To determine

To calculate: The area of the region bounded by graph of equations y=4x2 and y=x+2 by using double integration.

Explanation

Given Information:

The provided equations are y=4x2 and y=x+2.

Formula used:

If a region is R defined in the domain of ayb and cxd, then,

The area of the region R is,

A=cdabdydx

Calculation:

Consider the equations,

y=x,y=2x and x=2.

The graph of region bounded by the equation y=4x2 and y=x+2 is shown in below.

The point of intersection of the two graph is found by equating y=4x2 and y=x+2,

4x2=x+2x2+x2=0

Factor the above quadratic equation,

x2+2xx2=0x(x+2)1(x+2)=0(x+2)(x1)=0

Therefore,

x=1 and x=2

The point of intersection of the two graphs y=4x2 and y=x+2 is (2,0) and (1,3).

The bounds for x are 2x1 and bounds for y are 4x2yx+2

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