1. Tardigrade
  2. Question
  3. Mathematics
  4. The average value of a function f ( x ) over the interval, [ a , b ] is the number μ=(1/b-a) ∫ limitsab f(x) d x The square root (1/b-a) ∫ limitsab[f(x)]2 d x 1 / 2 is called the root mean square of f on [ a, b]. The average value of μ is attained if f is continuous on [a, b]. The average value of f(x)=( cos 2 x/ sin 2 x+4 cos 2 x) on [0, π / 2] is -

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Q. The average value of a function $f ( x )$ over the interval, $[ a , b ]$ is the number
$\mu=\frac{1}{b-a} \int\limits_a^b f(x) d x$
The square root $\left\{\frac{1}{b-a} \int\limits_a^b[f(x)]^2 d x\right\}^{1 / 2}$ is called the root mean square of $f$ on $[ a, b].$ The average value of $\mu$ is attained if $f$ is continuous on $[a, b]$.
The average value of $f(x)=\frac{\cos ^2 x}{\sin ^2 x+4 \cos ^2 x}$ on $[0, \pi / 2]$ is -

Integrals

Solution:

Correct answer is (a) $\pi / 6$