   Chapter 7.8, Problem 6CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Use a double integral to calculate the area denoted by ∫ R ∫ d A where R is the region bounded by y   =   2 x +   3  and  y = x 2 .

To determine

To calculate: The area A bounded by the region R for y=2x+3 and y=x2.

Explanation

Formula used:

The area of the region R is given by,

RdA=Rdxdy

Where dA=dxdy or dydx.

Calculation:

To calculate the area A bounded by the region R for y=2x+3 and y=x2, first draw the sketch of both the functions,

Consider the function y=2x+3,

Choose some values for x and compute the value for y, in order to form the ordered pairs.

Put x=0 in the function y=2x+3. Then,

y=3

Put x=1 in the function y=2x+3. Then,

y=2x+3=2(1)+3=5

Put x=1 in the function y=2x+3. Then,

y=2x+3=2(1)+3=2+3=1

The required table is shown below,

 x y (x,y) 0 3 (0,3) 1 5 (1,5) −1 1 (−1,1)

Plot these ordered pairs on the graph and join them with a straight line.

Now, consider the function y=x2,

Now, choose some values for x and compute the value for y in order to form the ordered pairs that will plot on the graph.

Now, put x=0 in the equation y=x2.

y=x2=(0)2=0

Now, put x=1 in the equation y=x2.

y=x2=(1)2=1

Now, put x=1 in the equation y=x2.

y=x2=(1)2=1

Now, put x=3 in the equation y=x2.

y=x2=(3)2=9

Now, put x=3 in the equation y=x2.

y=x2=(3)2=9

The required table is shown below,

 x y=x2−4x+3 (x,y) 0 0 (0,0) 1 1 (1,1) −1 1 (−1,1) 3 9 (3,9) −3 9 (−3,9)

Plot these ordered pairs on the graph and join them with a free hand

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