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

`1`

B

`0`

C

`-1`

D

`pi`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (LEVEL 2 ) Single Correct Answer Type Questions|33 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Numerical Answer Type Questions)|16 Videos

  • DEFINITE INTEGRALS

    MCGROW HILL PUBLICATION|Exercise SOLVED EXAMPLES (Concept-based) Single Correct Answer Type Questions|10 Videos

  • COMPLEX NUMBERS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS. B-ARCHITECTURE ENTRANCE EXAMINATION PAPER|17 Videos

  • DETERMINANTS

    MCGROW HILL PUBLICATION|Exercise QUESTIONS FROM PREVIOUS YEARS B-ARCHITECTURE ENTRANCE EXAMINATION PAPERS|18 Videos

Similar Questions

Explore conceptually related problems

Let f:R rarr R and g:R rarr 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

Let f:R rarr and g:R rarr R be continuous function.Then the value of the integral int_(-(pi)/(2))^((pi)/(2))[f(x)+f(-x)][g(x)-g(-x)]dx is pi (b) 1(c)-1(d)0

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

Let f: R to R be a continuous function. Then lim_(x to pi//4) (pi/4 int_2^(sec^2x) f(x)dx)/(x^2 - pi^2/16) is equal to :

Let f: R to R be a continuous function. Then lim_(x to pi//4) (pi/4 int_2^(sec^2x) f(x)dx)/(x^2 - pi^2/16) is equal to :

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

Let f : R rarr R and g : R rarr R be two functions such that fog (x) = sin x^(2) and gof (x) = sin^(2)x . Then , find f(x) and g(x).

MCGROW HILL PUBLICATION-DEFINITE INTEGRALS-SOLVED EXAMPLES (LEVEL 1 ) Single Correct Answer Type Questions
  1. int0^1x(1-x)^(99)dx=

    Text Solution

    |

  2. The value of sum(n=1)^1000 int(n-1)^n e^(x-[x])dx, where [x] is the gr...

    Text Solution

    |

  3. Let f : R -> R and g : R -> R be continuous functions. Then the value...

    Text Solution

    |

  4. If f(x) = (1+ tanx) (1+ tan (pi//4 - x)) and g(x) is a function with d...

    Text Solution

    |

  5. Find lim(n->oo) Sn ; if Sn=1/(2n)+1/(sqrt(4n^2-1))+1/(sqrt(4n^2-...

    Text Solution

    |

  6. Evaluate: int(-pi)^(3pi)log(s e ctheta-t a ntheta)dtheta

    Text Solution

    |

  7. The value of int(0)^(oo) (dx)/((x^(2)+4)(x^(2)+9) ) is

    Text Solution

    |

  8. Evaluate int-1 3/2|xsin(pix)|dx

    Text Solution

    |

  9. If f(0)=2, f'(x) =f(x), phi (x) = x+f(x) then int(0)^(1) f(x) phi (x) ...

    Text Solution

    |

  10. Evaluate: ("lim")(xvec2)(int0"x"cost^2dt)/x

    Text Solution

    |

  11. If f(x) =int(1//x^(2) ) ^(x^2) cos sqrt(t) dt, then f'(1) is equal to

    Text Solution

    |

  12. The least value of the function phi(x)=overset(x)underset(5pi//4)int...

    Text Solution

    |

  13. Evaluate int0^a(log(1+a x)/(1+x^2)dx)

    Text Solution

    |

  14. If I(m,n)= overset(1)underset(0)int x^(m) (ln x)^(n)dx then I(m,n) i...

    Text Solution

    |

  15. If I(n) = int(0)^(1) ( cos^(-1) x)^(n) dx then I(6)- 360 I(2) is given...

    Text Solution

    |

  16. If I(n)=underset(0)overset(pi//2)int x^(n) sin x dx, then I(4)+12I(2) ...

    Text Solution

    |

  17. If a function f: [ 0, 27] to R is differentiable then for some 0 lt al...

    Text Solution

    |

  18. The difference between the greatest and least values of f(x)= int0^x (...

    Text Solution

    |

  19. The value of the integral overset(pi//4)underset(0)int (sinx+cosx)/(3+...

    Text Solution

    |

  20. Find the points of minima for f(x)=int0^x t(t-1)(t-2)dt

    Text Solution

    |