Home
Class 12
MATHS
If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e...

If `f(x)=f(pi+e-x) and int_e^pif(x)dx=2/(e+pi),` then `int_e^pi xf(x)dx` is equal to

A

`pi-e`

B

`(pi+e)/2`

C

`1`

D

`(pi-e)/2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise EVALUATIO TEST|30 Videos
  • DEFINITE INTEGRALS

    TARGET PUBLICATION|Exercise CRITICAL THINKING|115 Videos
  • CONTINUITY

    TARGET PUBLICATION|Exercise Evaluation Test|10 Videos
  • DIFFERENTIAL EQUATIONS

    TARGET PUBLICATION|Exercise EVALUATION TEST|25 Videos

Similar Questions

Explore conceptually related problems

If f(x)=f(pi+e-x) and int_(e)^( pi)f(x)dx=(2)/(e+pi) then int_(e)^( pi)xf(x)dx is equal to

int e^(x){f(x)-f'(x)}dx=phi(x), then int e^(x)f(x)dx is

int_(-pi)^( pi)sin x[f(cos x)]dx is equal to

If int(e^(x)-1)/(e^(x)+1)dx=f(x)+C, then f(x) is equal to

What is int_(0)^(pi)e^(x) sin x dx equal to ?

int_(0)^( pi)xf(sin x)dx=(pi)/(2)int_(0)^( pi)f(sin x)dx

If inte^(2x)f'(x)dx=g(x) , then int[e^(2x)f(x)+e^(2x)f'(x)]dx=

If int_(0)^(oo)(dx)/(e^(x)+e^(-x))=(pi)/(k) then k is equal to

I=int_(0)^(2)(e^(f(x)))/(e^(f(x))+e^(f(2-x)))dx is equal to

solve int_(0)^( pi)e^(x)dx

TARGET PUBLICATION-DEFINITE INTEGRALS-COMPETITIVE THINKING
  1. The value of the integral I = int(1//2014)^(2014)(tan^(-1) x)/x dx is

    Text Solution

    |

  2. The value of the definite integral 1/pi int(pi/2)^((5pi)/2) e^(tan^(-...

    Text Solution

    |

  3. If f(x)=f(pi+e-x) and inte^pif(x)dx=2/(e+pi), then inte^pi xf(x)dx is ...

    Text Solution

    |

  4. The value of int(pi//4)^(3pi//4)(phi)/(1+sinphi)d phi is

    Text Solution

    |

  5. Let I(1) =int(a)^(pi-a)xf(sinx)dx,I(2)=int(a)^(pi-a)f(sinx)dx, then I(...

    Text Solution

    |

  6. If f(x)=(e^(2))/(1+e^(x)),I(1)=overset(f(a))underset(f(-a))int xg{x(1-...

    Text Solution

    |

  7. Q. int0^pi(e^(cos^2x)( cos^3(2n+1) x dx, n in I

    Text Solution

    |

  8. int0^pi x f(sin x)dx is equal to

    Text Solution

    |

  9. If I(1)=int(0)^(pi//2)f(sin2x)sin x dx and I(2)=int(0)^(pi//4)f(cos2x)...

    Text Solution

    |

  10. Evaluate: int0^(100pi)sqrt((1-cos2x))dxdot

    Text Solution

    |

  11. int(-1)^(1) sin^(3) x cos^(2) x dx is equal to

    Text Solution

    |

  12. The value of int((pi)/4)/((-pi)/4)sin^(103)x .cos^(101)xdx is

    Text Solution

    |

  13. The value of int- 2^2(xcosx+sinx+1)dx is

    Text Solution

    |

  14. int(4)^(4)log((9-x)/(9+x))dx equals

    Text Solution

    |

  15. Evaluate the following : int(-pi//2)^(pi//2)log((2-sinx)/(2+sinx))d...

    Text Solution

    |

  16. To find the numberical value of overset(2)underset(-2)int (px^(3)+qx+8...

    Text Solution

    |

  17. If f(x)={(e^(cosx)sinx, |x|le2),(2, otherwise):} then int-2^3f(x)dx= (...

    Text Solution

    |

  18. int(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dxi se q u a lto -4 (b) 0 (c...

    Text Solution

    |

  19. If f(x) is defined on [-2, 2] by f(x) = 4x^2 – 3x + 1 and g(x) = (f(-x...

    Text Solution

    |

  20. int-2^2 |x| dx is equal to

    Text Solution

    |