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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

Find the area between the curves in Problems 19-22.

y = x 2 3 x + 2  and  y = x 2 + 4   from  x = 0  to  x = 5

To determine

To calculate: The area under the graph of y=x23x+2 and y=x2+4 from x=0 to x=5 using the definite integral method.

Explanation

Given Information:

The provided functions are y=x23x+2 and y=x2+4 and range of x is 0x5.

Formula Used:

The area between two graphs:

If f(x)g(x) for all x in [a,b] (so that the graph of f doesn’t move below that of g), then the area of the region between the graphs of f and g and between x=a and x=b is given by:

A=ab[f(x)g(x)dx]

Calculation:

The provided functions are y=x23x+2 and y=x2+4 and range of x is 0x5.

The point of intersection can be obtained by keeping them equal:

x23x+2=x2+43x+2=43x=2x=23

The point of intersection is x=23.

Consider the equation y=x23x+2.

Substitute x=0 in y=x23x+2.

y=(0)23(0)+2=2

Substitute x=1 in y=x23x+2.

y=(1)23(1)+2=0

Substitute x=3 in y=x23x+2.

y=(3)23(3)+2=99+2=2

Summarized all points in a table,

x y (x,y)
0 2 (0,2)
1 0 (1,0)
3 2 (3,2)

Now, consider the equation y=x2+4.

Substitute x=0 in y=x2+4.

y=(0)2+4=4

Substitute x=1 in y=x2+4

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