   Chapter 12.2, Problem 80E

Chapter
Section
Textbook Problem

# True or False? In Exercises 73-76, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The definite integral of a vector-valued function is a real number.

To determine
Whether the statement “The definite integral of a vector-valued function is a real number” is true or false.

Explanation

The provided statement “The definite integral of a vector-valued function is a real number” is false.

Example:

Let f(t)=ti+t2j+2tk is a vector valued function.

Now, first integrate the function with limits from 0 to 1.

01f(t)dt=01tdt i+01t2dt j+<

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