# Calculating the Average Value of cos^2(x) [0,(pi/4)]

• Allie G
In summary, to find the average value of cos^2(x) from 0 to pi/4, the correct solution is (2/pi)[x+sin2x/2] from pi/4 to 0, which equals (1/pi)+(1/2). The incorrect solution given was 1.
Allie G

## Homework Statement

find the average value of cos^2(x) [0,(pi/4)]

## Homework Equations

I don't think I'm doing it correctly I know the formula,(I won't put my attempt because I don't have math symbols on my computer) but I get 1 as the answer every time which doesn't seem correct

## The Attempt at a Solution

You should try to give your attempt.
or "Quote" an earlier post, you'll see a small $$\Sigma$$ symbol, which will help you compose the mathematical symbols.

ok so my attempt is
(4/pi)$$\int\overline{}4/pi$$$$\underline{}0$$(1/2)(1+cos2x)

(2/pi)[x+sin2x/2]$$\overline{}pi/4$$$$\underline{}0$$

(2/pi)[(pi/4+(1/2)=1

hmm I am sorry I am new i don't think i can get it right the 4/pi is the upper bound the 0 is the lower bound

Allie G said:
ok so my attempt is
(4/pi)$$\int\overline{}4/pi$$$$\underline{}0$$(1/2)(1+cos2x)

(2/pi)[x+sin2x/2]$$\overline{}pi/4$$$$\underline{}0$$

(2/pi)[(pi/4+(1/2)=1

Don't worry about the formatting. Better luck next time. But you are doing great! Except (2/pi)[pi/4+(1/2)] doesn't equal 1. Notice where I put the brackets.

Last edited:
Dick said:
Don't worry about the formatting. Better luck next time. But you are doing great! Except (2/pi)[pi/4+(1/2)] doesn't equal 1. Notice where I put the brackets.

Soo that would be equal to
(1/pi)+(1/2)?

Allie G said:
Soo that would be equal to
(1/pi)+(1/2)?

Yessss. It would. That's 0.8183... Not 1.

thank you so much

## What is the formula for calculating the average value of cos^2(x) [0,(pi/4)]?

The formula for calculating the average value of cos^2(x) [0,(pi/4)] is:
avg = (1/(b-a))*∫abcos^2(x) dx, where a = 0 and b = (pi/4).

## How do you find the average value of cos^2(x) [0,(pi/4)]?

To find the average value of cos^2(x) [0,(pi/4)], you need to integrate cos^2(x) from 0 to (pi/4) and then divide the result by the length of the interval, which is (pi/4 - 0) = (pi/4).

## What is the range of cos^2(x)?

The range of cos^2(x) is [0,1]. This means that the values of cos^2(x) can range from 0 to 1, inclusive.

## Can the average value of cos^2(x) [0,(pi/4)] be negative?

No, the average value of cos^2(x) [0,(pi/4)] cannot be negative. This is because cos^2(x) is always positive on the interval [0,(pi/4)] and the average value is calculated by taking the mean of all the values within that interval.

## What is the significance of calculating the average value of cos^2(x) [0,(pi/4)]?

Calculating the average value of cos^2(x) [0,(pi/4)] is useful in various applications, such as in calculating the average power in an AC circuit or in finding the average brightness of a light source. It also helps in understanding the behavior of the function over a specific interval and can be used to compare different functions in terms of their average values.

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