   Chapter 4.3, Problem 64E

Chapter
Section
Textbook Problem

True or False? In Exercises 63-68, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. ∫ a b f ( x ) g ( x ) d x = [ ∫ a b f ( x ) d x ] [ ∫ a b g ( x ) d x ]

To determine
Whether the provided statement ab[f(x)g(x)]dx=[abf(x)dx][abg(x)dx] is true or false.

Explanation

Given:

The provided statement is

ab[f(x)g(x)]dx=[abf(x)dx][abg(x)dx]

Explanation:

Take f(x)=x and g(x)=4x.

The left hand side of the provided expression is

ab(f(x)g(x))dx

We will put the value of f(x) and g(x)

we get,

ab(f(x)g(x))dx=abx(4x)dx=ab4x2dx

Factor out 4

=4abx2dx

We will apply, abxndx=(xn+1n+1)

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