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

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.
  • #1
Allie G
7
0

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

 
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  • #2
You should try to give your attempt.
If you select "Go Advanced" during a Quick Reply
or "Quote" an earlier post, you'll see a small [tex]\Sigma[/tex] symbol, which will help you compose the mathematical symbols.
 
  • #3
ok so my attempt is
(4/pi)[tex]\int\overline{}4/pi[/tex][tex]\underline{}0[/tex](1/2)(1+cos2x)

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

(2/pi)[(pi/4+(1/2)=1
 
  • #4
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
 
  • #5
Allie G said:
ok so my attempt is
(4/pi)[tex]\int\overline{}4/pi[/tex][tex]\underline{}0[/tex](1/2)(1+cos2x)

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

(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:
  • #6
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)?
 
  • #7
Allie G said:
Soo that would be equal to
(1/pi)+(1/2)?

Yessss. It would. That's 0.8183... Not 1.
 
  • #8
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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