Average value of sin(x) integral of sin(x)/x

In summary, the conversation discusses the average value of sin(x) between 0 and pi/2, and how it can be calculated using the integral of sin(x) over those bounds. The conversation also mentions using MATLAB to solve this problem and provides a resource for more information on calculating the average value of a function.
  • #1
NoobixCube
155
0
This isn't a homework question by the way
I was trying to think what the average value of sin(x) was between 0 and pi/2.
I came to the conclusion it must be integral of sin(x)/x evaluated at those bounds. But I tried to do that in MATLAB to no avail.
Any help would be awesome
 
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  • #2
How did you come to that conclusion? The average value of sin(x) between pi/2 and 0 is the integral of sin(x) from 0 to pi/2 divided by pi/2. See http://archives.math.utk.edu/visual.calculus/5/average.1/index.html.
 
  • #3


thanks for your reply. Brain was clearly switched off and now I feel foolish :blushing:
 

1. What is the formula for calculating the average value of sin(x)?

The average value of sin(x) can be calculated by taking the integral of sin(x) from 0 to 2π (or any multiple of π) and dividing it by the length of the interval, in this case, 2π. This can be represented by the formula:
Average value of sin(x) = (1/2π)∫sin(x)dx from 0 to 2π.

2. Why is the average value of sin(x) equal to zero?

The average value of sin(x) is not always equal to zero. However, it is equal to zero when the integral of sin(x) over a full period (from 0 to 2π or any multiple of π) is equal to zero. This is because the positive and negative values of sin(x) cancel each other out when integrated over a full period, resulting in an average value of zero.

3. Can the average value of sin(x) be negative?

Yes, the average value of sin(x) can be negative. This can occur when the integral of sin(x) over a full period is negative. In other words, when the negative values of sin(x) outweigh the positive values over the interval, the average value will be negative.

4. What is the significance of calculating the average value of sin(x)?

The average value of sin(x) is important in many applications, such as signal processing and harmonic analysis. It allows us to determine the average behavior of a periodic function over a given interval, which can provide valuable insights and make calculations easier.

5. Can the average value of sin(x) be used to find the area under the curve?

No, the average value of sin(x) cannot be used to find the area under the curve. This is because the average value is only a single value, while the area under the curve is a measure of the total space enclosed by the curve and the x-axis. To find the area under the curve, we would need to calculate the integral of sin(x) over a specific interval.

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