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The average value of a function f(x) ove...

The average value of a function `f(x)` over the interval `[a,b]` is the number `mu=(1)/(b-a)int_(a)^(b)f(x)dx`. The square root `{(1)/(b-a)int_(a)^(b)f^(2)(x)dx}^((1)/(2))` is called the root mean square of `f` on `[a,b]`. The average value `mu` is attained if `f` is continuous on `[a,b]`.
The average value of `f(x)=(cos^(2)x)/(sin^(2)x+4cos^(2)x)` on `[0,(pi)/(2)]` is

A

`(pi)/(6)`

B

`(4)/(pi)`

C

`(6)/(pi)`

D

`(1)/(6)`

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