   Chapter 15, Problem 3P

Chapter
Section
Textbook Problem

Find the average value of the function f ( x ) = ∫ x 1 cos ( t 2 )   d t on the interval [0, 1].

To determine

The average value of the function f(x)=x1cos(t2)dt.

Explanation

Given:

The function, f(x)=x1cos(t2)dt on the interval [0,1].

Formula used:

The average of the given function is given by, fave=1baabf(x)dx.

Calculation:

Here, a=0,b=1. Thus, the average value becomes,

fave=11001(x1cos(t2)dt)dx=1101(0tcos(t2)dx)

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