   Chapter 13.3, Problem 26E ### Mathematical Applications for the ...

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

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

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

# In Problems 13-26, equations are given whose graphs enclose a region. In each problem, find the area of the region. y = 4 − x ;   x = 4 ; ​   y = 3

To determine

To calculate: The area of the region between y=4x, x=4 and y=3.

Explanation

Given information:

The provided curve is:

y=4x, x=4 and y=3.

Formula used:

Area between two curve:

If f and g are continuous functions on [a,b] and if f(x)g(x) on [a,b], then the area of the region bounded by y=f(x), y=g(x), x=a, and x=b is:

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

Or

A=Integral of (Top Bottom)

Calculation:

Consider the provided equation:

y=4x, x=4 and y=3

Draw the graph of the above function to check whether f(x)g(x):

Calculate the values at different values of x:

Substitute x=0 in the function y=4x.

y=40=2

Substitute x=1 in the function y=4x.

y=41=1.73

Substitute x=2 in the function y=4x.

y=42=1.41

Substitute x=1 in the function y=4x.

y=4(1)=2.23

The table provided below shows the values of the function at different values of x.

 x y=x+3 Coordinates (x,y) 0 2 (0,2) 1 1.73 (1,1.73) 2 1.41 (2,1

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