Home
Class 12
MATHS
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)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Assertion-Reason Type Questions|15 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Integar Type Questions|8 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (More than one answer)|32 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

If f(a+b-x) =f(x) , then int_(a)^(b) x f(x) dx is equal to

If int_(a)^(b)f(dx)dx=l_(1), int_(a)^(b)g(x)dx = l_(2) then :

Suppose f is continuous on [a,b] & f(a)=f(b)=0 & int_(a)^(b)f^(2)(x)dx=1 then the minimum value of int_(a)^(0)(f^(')(x))^(2)dx int_(a)^(b) x^(2)f^(2)(x)dx is k , then 8k is

Given a real valued fuction f(x) which is monotonic and differentiable , prove that for any real number a and b, int_(a)^(b){f^(2)(x)-f^(2)(a)} dx = int_(f(a))^(f(b))2x{b-f^(-1)(x)} dx

If f(x) is continuous and int_(0)^(9)f(x)dx=4 , then the value of the integral int_(0)^(3)x.f(x^(2))dx is

Let f(x) be a differentiable function in the interval (0, 2) then the value of int_(0)^(2)f(x)dx

If I_(1)=int_(3pi)^(0) f(cos^(2)x)dx and I_(2)=int_(pi)^(0) f(cos^(2)x) then

If the range of the function f(x)= cot^(-1)((x^(2))/(x^(2)+1)) is (a, b), find the value of ((b)/(a)+2) .

If | int_(a)^(b) f(x)dx|= int_(a)^(b)|f(x)|dx,a ltb,"then " f(x)=0 has

If f(x)=f(a+b-x) for all x in[a,b] and int_(a)^(b) xf(x) dx=k int_(a)^(b) f(x) dx , then the value of k, is