Home
Class 12
MATHS
Let f and g be continuous fuctions on [0...

Let f and g be continuous fuctions on [0, a] such that `f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " underset0oversetaintf(x)g(x)dx` is equal to

A

`4 int_(0)^(a)f(x)dx`

B

`int_(0)^(a)f(x)dx`

C

`-3int_(0)^(a)f(x)dx`

D

`2int_(0)^(a)f(x)dx`

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 Advanced (Archive)|103 Videos

  • INTEGRAL CALCULUS - 2

    VMC MODULES ENGLISH|Exercise Level - 1|190 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

Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" and "g(x)+g(a-x)=4 " then " int_(0)^(a)f(x)g(x)dx is equal to

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 (d)/(dx)f(x)=g(x) for a le x le b then, overset(b)underset(a)int f(x) g(x) dx equals

f,g, h , are continuous in [0, a],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5. Then prove that int_0^af(x)g(x)h(x)dx=0

Let f and g be two differentiable functions on R such that f'(x)>0 and g′(x) g(f(x-1)) (b) f(g(x))>f(g(x+1)) (c) g(f(x+1))

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,

Let f(x) and g(x) be two functions satisfying f(x^(2))+g(4-x)=4x^(3), g(4-x)+g(x)=0 , then the value of int_(-4)^(4)f(x^(2))dx is :

f(x) and g(x) are two differentiable functions in [0,2] such that f"(x)=g"(x)=0, f'(1)=2, g'(1)=4, f(2)=3, g(2)=9 then f(x)-g(x) at x=3/2 is

If f(x)=x+tanx and f is inverse of g, then g ′(x) is equal to

The value of int [f(x)g''(x) - f''(x)g(x)] dx is equal to

VMC MODULES ENGLISH-INTEGRAL CALCULUS - 2 -JEE Main (Archive)
  1. The integral int(pi//6)^(pi//4)dx/(sin2x(tan^5x+cot^5x))equal

    Text Solution

    |

  2. The area (in sq. units) of the region bounded by the parabola y=x^2+2"...

    Text Solution

    |

  3. Let f and g be continuous fuctions on [0, a] such that f(x)=f(a-x)" an...

    Text Solution

    |

  4. The integral underset1overseteint{(x/e)^(2x)-(e/x)^x}logexdx is equal ...

    Text Solution

    |

  5. The area (in sq. units) of the region A={(x,y)in R xx R |0 le x le 3, ...

    Text Solution

    |

  6. If f(x)=(2-xcosx)/(2+xcosx)andg(x)= "log"(e)x, (xgt0) then the value ...

    Text Solution

    |

  7. Let f ( x) = int 0 ^ x g (t) dt , where g is a non - ze...

    Text Solution

    |

  8. Let f(x,y) = {(x,y): y^(2) le 4x,0 le x le lambda} and s(lambda) is a...

    Text Solution

    |

  9. int(0)^((pi)/(2))(sin^(3)x)/(sinx+cosx)dx is equal to

    Text Solution

    |

  10. The area (in sq. units) of the region {(x,y) in R^(2) : x^(2) le y le ...

    Text Solution

    |

  11. The value of the integral int(0)^(1)xcot^(-1)(1-x^(2)+x^(4))dx is

    Text Solution

    |

  12. The area (in sq. units) of the region A = {(x,y), y^(2)//2 le x le y +...

    Text Solution

    |

  13. The value of int(0)^(2pi)[sin2x (1+cos 3x)]dx, where [t] denotes the g...

    Text Solution

    |

  14. The region represented by |x-y|le 2 and |x +y| le 2 is bounded by a:

    Text Solution

    |

  15. The integral int sec^(2//3)x cosec^(4//3)x dx is equal to : (Here ...

    Text Solution

    |

  16. The area (in sq. units) of the region bounded by the curves y=2^(x) an...

    Text Solution

    |

  17. If int(0)^(pi//2) (cot x)/(cot x+cosecx)dx=m(pi+n), then m*n is equal ...

    Text Solution

    |

  18. If the area (in sq. units) of the region {(x,y): y^(2) lt= 4x,x+y lt...

    Text Solution

    |

  19. Let f : R to R be a continuously differentiable function such that f(...

    Text Solution

    |

  20. A value of alpha such that int(alpha)^(alpha+1) (dx)/((x+a)(x+...

    Text Solution

    |