Home
Class 12
MATHS
Let f: Rveca n dg: RvecR be continuous f...

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

A

`pi`

B

1

C

`-1`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|64 Videos
  • FUNCTIONS

    VMC MODULES ENGLISH|Exercise JEE Main & Advanced|8 Videos
  • INTEGRAL CALCULUS-1

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|25 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_(0)^(pi//2)(f(x))/(f(x)+f(pi/(2)-x))dx is

If f(x)=(2-xcosx)/(2+xcosx)andg(x)= "log"_(e)x, (xgt0) then the value of the integral int_(-pi//4)^(pi//4)g(f(x)) dx is

If f(x)=x+sinx , then find the value of int_pi^(2pi)f^(-1)(x)dx .

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:[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:

If f(x)a n dg(x) are continuous functions, then int_(1nlambda)^(1n1/lambda)(f((x^2)/4)[f(x)-f(-x)])/(g((x^2)/4)[g(x)+g(-x)])dxi s (a)dependent on lambda (b) a none-zero constant (c)zero (d) none of these

Let f: RvecR and g: Rvec be two functions such that fog(x)=sinx^2a n d gof(x)= sin^2x dot Then, find f(x)a n dg(x)dot

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

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

Let f: Rveca n dg: RvecR be defined by f(x)=x+1a n dg(x)=x-1. Show that fog=gof=I_Rdot

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Advanced (Archive)
  1. The value of int(0)^(2pi)[2 sin x]dx, where [.] represent the greatest...

    Text Solution

    |

  2. If f(x)=Asin((pix)/2)+b ,f^(prime)(1/2)=sqrt(2)a n d int0^1f(x)dx=(2A...

    Text Solution

    |

  3. Let f: Rveca n dg: RvecR be continuous function. Then the value of the...

    Text Solution

    |

  4. For any integer n,the integral overset(pi)underset(0)int e^(sin^(2)x)c...

    Text Solution

    |

  5. Suppose we define integral using the following formula int(a)^(b)f(x)d...

    Text Solution

    |

  6. Let the definite integral be defined by the formula int(a)^(b)f(x)dx=(...

    Text Solution

    |

  7. Suppose we define integral using the following formula int(a)^(b)f(x)d...

    Text Solution

    |

  8. The value of int(0)^(1)(x^(4)(1-x)^(4))/(1+x^(4))dx is (are)

    Text Solution

    |

  9. If int(n)=int(-pi)^(pi)(sin nx)/((1+pi^(x))sinx) dx, n=0,1,2,………. then

    Text Solution

    |

  10. Let f:[1,oo] be a differentiable function such that f(1)=2. If int1...

    Text Solution

    |

  11. Let d/(dx)F(x)=(e^(sinx))/x . x lt0. If int(1)^(4)(2e^(sinx^(2)))/xdx=...

    Text Solution

    |

  12. int(1)^(e^(37))(pisin(pilogx))/(x)dx equals to.

    Text Solution

    |

  13. Prove that: int0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx

    Text Solution

    |

  14. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dxi s

    Text Solution

    |

  15. The value of overset(3pi//4)underset(pi//4)int (x)/(1+sin x) dx is equ...

    Text Solution

    |

  16. The value of int(-2)^2|1-x^2|dx is

    Text Solution

    |

  17. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  18. Match the conditions // expression in Column I with statement in Colum...

    Text Solution

    |

  19. Match List I with List II and select the correct answer using the code...

    Text Solution

    |

  20. Evaluate: 5050(int0 1(1-x^(50))^(100)dx)/(int0 1(1-x^(50))^(101)dx)

    Text Solution

    |