   Chapter 13.3, Problem 1CP ### 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

# True or false:(a) Over the interval [a, b], the area between the continuous functions f(x) and g(x) is ∫ a b [ f ( x ) - g ( x ) ] d x (b) If f ( x )   ≥   g ( x ) and the area between f(x) and £(x) is given by then x = a and x = b represent the left and right boundaries, respectively, of the region.(c) To find points of intersection of f ( x )  and  g ( x ) ,  solve  f ( x )   = g ( x ) .

(a)

To determine

Whether the provided statement “Over the interval [a,b] the area between the continuous function f(x) and g(x) is ab[f(x)g(x)]dx” is true or false.

Explanation

Given information:

The provided statement is:

Over the interval [a,b] the area between the continuous function f(x) and g(x) is ab[f(x)g(x)]dx

Explanation:

Consider the formula of area between the two curves:

If f and g are continuous functions on [a,b] and if f(x)g(x) for all x in [a,b] then the area of the region between the graphs of f and g are given and between x=a and x=b is given by:

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

(b)

To determine

Whether the provided statement “If f(x)g(x) and the area between the curve is given by ab[f(x)g(x)]dx then x=a and x=b represents the left and right boundary respectively, of the region” is true or false.

(c)

To determine

Whether the provided statement “To find the point of intersection of f(x) and g(x)” is true or false.

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