Question

The average value of a function $f(x)$ over the interval, $[a,b]$ is the number
$\mu =\frac{1}{b-a}\underset{a}{\overset{b}{\int }}f(x)dx$
The square root ${\left\{\frac{1}{b-a}\underset{a}{\overset{b}{\int }}[f(x){]}^{2}dx\right\}}^{1/2}$ 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 -

• A. $\pi /6$
• B. $4/\pi$
• C. $6/\pi$
• D. $1/6$

Answer 1

Answer: (A)

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