October 2004:
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October 2004: | |
The average of the cos2 function is very important in physcial applications of mathematics. Verify that the value of this average is 1/2. | |
Intuitively, the cosine square function is a positive oscillating function varying between 0 to 1. The average makes sense to be 1/2. However, this has to be verified using calculus. We can take this average from 0 to 2pi. To do this, we integrate cos2 and divide the result by 2pi. The result of the integral is pi and thus pi/2pi is 1/2. The average can be taken from any multiple of pi to another and the same result yields. Topic: Calculus
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