Home
Class 12
MATHS
Let f : R -> R and g : R -> R be contin...

Let `f : R -> R` and `g : R -> R` be continuous functions. Then the value of the integral `int_(pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dx` is

A

`pi`

B

`1`

C

`-1`

D

`0`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (Only one answer)|70 Videos

  • INTEGRALS

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

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Try yourself|50 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

Let f: Rveca n dg: RvecR be continuous function. Then the value of the integral int_(-pi/2)^(pi/2)[f(x)+f(-x)][g(x)-g(-x)]dxi s (a) pi (b) 1 (c) -1 (d) 0

If f(x) and g(x) are two continuous functions defined on [-a,a] then the the value of int_(-a)^(a) {f(x)f+(-x) } {g(x)-g(-x)}dx is,

If f(x) and g(x) are continuous functions, then int_(In lamda)^(In (1//lamda))(f(x^(2)//4)[f(x)-f(-x)])/(g(x^(2)//4)[g(x)+g(-x)])dx is

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in R . If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to

Let f:R in R be a continuous function such that f(1)=2. If lim_(x to 1) int_(2)^(f(x)) (2t)/(x-1)dt=4 , then the value of f'(1) is

Let f:R in R be a continuous function such that f(x) is not identically equal to zero. If int_(0)^(x) |x-2|dx,x ge 0 . Then, f'(x) is

If f and g are continuous functions on [ 0, pi] satisfying f(x) +f(pi-x) =1=g (x)+g(pi-x) then int_(0)^(pi) [f(x)+g(x)] dx is equal to

Let f: R->R , g: R->R be two functions defined by f(x)=x^2+x+1 and g(x)=1-x^2 . Write fog\ (-2) .

Let f:[0,1]to R be a continuous function then the maximum value of int_(0)^(1)f(x).x^(2)dx-int_(0)^(1)x.(f(x))^(2)dx for all such function(s) is:

Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show that fog!=gofdot