FINDING AREAS BY INTEGRATING
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Examples.
(1) To find the quadratic mean of the function (Fig. 63).
Here the integral is , which is .
Dividing by and taking the square root, we have
quadratic mean .
Here the arithmetical mean is ; and the ratio of quadratic to arithmetical mean (this ratio is called the form-factor) is .
(2) To find the quadratic mean of the function .
The integral is , that is .
Hence quadratic mean .
(3) To find the quadratic mean of the function
The integral is , that is ,