Chapter 7: Q12P (page 350)

To find the average value of the function on the given interval.
$c o s^{2} \frac{7 πx}{2} o n (0, \frac{8}{7})$ .

Short Answer

Expert verified

The average value of the given function over two periods is $\frac{1}{2}$ .

Step by step solution

Given

The given function on the interval is $\cos^{2} \frac{7 π x}{2} o n (0, \frac{8}{7})$ .

The concept of the average value of a function over a particular interva

The average value of a function over a particular interval can be found with an expression involving an integral.

Let's say that interval is $[a, b |$ .

Then the average value off(x)over said interval is $\frac{1}{b - a} \int_{a}^{b} f (x) d x$ .

Averagefunction on the given interval

From the given information, the average value is zero since all the functions are periodic with periods $T = \frac{8}{7}$ .

The average function on the given interval is shown below.

$= \int_{0}^{8 / 7} \cos^{2} \frac{7 π x}{2} d x$

The period of the function

The period of the function that is integrated is:

$\frac{2 π}{T} = \frac{7 π}{2} T = 4 / 7$

Thus, the average value of the given function over two periods is $\frac{1}{2}$ .

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To find the average value of the function on the given interval.
$c o s^{2} \frac{7 πx}{2} o n (0, \frac{8}{7})$ .

Short Answer

Step by step solution

Given

The concept of the average value of a function over a particular interva

Averagefunction on the given interval

The period of the function

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To find the average value of the function on the given interval.cos27πx2on(0,87).

Short Answer

Step by step solution

Given

The concept of the average value of a function over a particular interva

Averagefunction on the given interval

The period of the function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

Electromagnetism

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Fundamentals of Physics

Astrophysics

Study anywhere. Anytime. Across all devices.

To find the average value of the function on the given interval.
$c o s^{2} \frac{7 πx}{2} o n (0, \frac{8}{7})$ .