Home
Class 12
MATHS
If fa n dg are continuous function on [...

If `fa n dg` are continuous function on `[0,a]` satisfying `f(x)=f(a-x)a n dg(x)+g(a-x)=2,` then show that `int_0^af(x)g(x)dx=int_0^af(x)dxdot`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

Evaluate:If f(a-x)=f(x), then show that int_0^axf(x)dx=a/2int_0^af(x)dx

If f(2a-x)=-f(x) , then show that, int_(0)^(2a)f(x)dx=0

If f(x) and g(x) be continuous in the interval [0, a] and satisfy the conditions f(x)=f(a-x) and g(x)+g(a-x)=a , then show that int_(0)^(a)f(x)g(x)dx=(a)/(2)int_(0)^(a)f(x)dx . Hence find the value of int_(0)^(pi)xsinxdx .

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 a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

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)^(a)f(x)g(x)h(x)dx=0 .

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

int [f(x)g"(x) - f"(x)g(x)]dx is

Prove that int_(0)^(2a)f(x)dx=int_(0)^(a)[f(a-x)+f(a+x)]dx

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If the value of the definite integral int0^1 "^(207)C7x^(200)(1-x)^7dx...

    Text Solution

    |

  2. Evaluate: int(-1)^0(dx)/(x^2+2x+2)

    Text Solution

    |

  3. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a ...

    Text Solution

    |

  4. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

    Text Solution

    |

  5. Evaluate: int0^pie^(|cosx|)(2sin(1/2cosx)+3cos(1/2cosx))sinxdxdot

    Text Solution

    |

  6. Evaluate: inta^b x^3dx

    Text Solution

    |

  7. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

    Text Solution

    |

  8. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

    Text Solution

    |

  9. If y(x)=int(pi^2/16)^(x^2)(cosxcossqrt(theta))/(1+sin^2sqrt(theta))d t...

    Text Solution

    |

  10. Evaluate: underset(nrarrinfty)lim[(1/n^2sec^2(1/(n^2))+2/n^2sec^2((4)/...

    Text Solution

    |

  11. For x >0,l e tf(x)=int1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/...

    Text Solution

    |

  12. Evaluate ("lim")(n rarr oo)sum(k=1)^nk/(n^2+k^2)

    Text Solution

    |

  13. If" f, is a continuous function with int0^x f(t) dt->oo as |x|->ooth...

    Text Solution

    |

  14. Show that : pi/6leint0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt2)

    Text Solution

    |

  15. Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  16. Prove that int0^x e^(x t-t^2) dt=e^(x^(2)/4)int0^x e^-(t^(2)/4)dt

    Text Solution

    |

  17. If alpha=int0^1(e^(9x+3tan^-1x))((12+9x^2)/(1+x^2))dx where tan^-1x t...

    Text Solution

    |

  18. Evaluate int(-4)^(-5)e^((x+5)^(2))dx+3int(1//3)^(2//3)e^(9(x-2/3)^(2))...

    Text Solution

    |

  19. Prove that for any positive integer k ,(sin2k x)/(sinx)=2[cosx+cos3x+...

    Text Solution

    |

  20. Compute the integrals: int0^oof(x^n+x^(-n))logx(dx)/x

    Text Solution

    |