Home
Class 12
MATHS
If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)...

If `f(a+b-x)=f(x),\ t h e n\ int_a^b xf(x)dx` is equal to
a.`(a+b)/2int_a^bf(b-x)dx`
b. `(a+b)/2int_a^bf(b+x)dx`
c. `(b-1)/2int_a^bf(x)dx`
d. `(a+b)/2int_a^bf(x)dx`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA ENGLISH|Exercise All Questions|282 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA ENGLISH|Exercise All Questions|168 Videos

Similar Questions

Explore conceptually related problems

If f(a+b-x) =f(x) , then int_(a)^(b) x f(x) dx is equal to

If f(x)=f(a+b-x), then int_(a)^(b) xf(x)dx is equal to

int_(a)^(b) x dx

If f(a+b-x)=f(x),\ then prove that \ int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dx

int_(a+c)^(b+c) f(x) dx is equal to

int_a^b logx/x dx

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx =(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

If f(a+b-x)=f(x), then prove that int_a^b xf(x)dx=(a+b)/2int_a^bf(x)dxdot

RD SHARMA ENGLISH-DEFINITE INTEGRALS-All Questions
  1. Evaluate:int0^oolog(x+1/x)(dx)/(1+x^2)

    Text Solution

    |

  2. int0^(2a)f(x)dx is equal to a.2int0^af(x)dx b. 0 c. int0^af(x)dx+...

    Text Solution

    |

  3. If f(a+b-x)=f(x),\ t h e n\ inta^b xf(x)dx is equal to a.(a+b)/2inta^...

    Text Solution

    |

  4. The value of int0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ is a.1 b. -1 c....

    Text Solution

    |

  5. Choose the correct answer The value of int0pi/2log((4-3sinx)/(4+3cosx)...

    Text Solution

    |

  6. The value of int(-pi//2)^(pi//2)(x^3+x\ cos x+tan^5x+1)dx , is a. 2 b....

    Text Solution

    |

  7. Evaluate the following integral: int0^4x\ sqrt(4-x)\ dx

    Text Solution

    |

  8. Evaluate the following integral: int1^5x/(sqrt(2x-1))dx

    Text Solution

    |

  9. Evaluate the following integral: int0^1tan^(-1)x\ dx

    Text Solution

    |

  10. Evaluate the following integral: int0^1tan^(-1)((2x)/(1-x^2))dx

    Text Solution

    |

  11. Evaluate the following integral: int0^1(1-x)/(1+x)dx

    Text Solution

    |

  12. Evaluate the following integral: int0^(pi//2)(sin^2x)/((1+cos x)^2)dx

    Text Solution

    |

  13. Evaluate the following integral: int0^(pi//2)(cos x)/(1+sin^2x)dx

    Text Solution

    |

  14. Evaluate the following integrals: int0^1sqrt((1-x)/(1+x))dx

    Text Solution

    |

  15. Evaluate the following integral: int0^(pi//4)cos^4xsin^3x\ dx

    Text Solution

    |

  16. Evaluate the following integral: int0^(pi//2)x^2cos2x\ dx

    Text Solution

    |

  17. Evaluate the following integral: int2^4(x^2+x)/(sqrt(2x+1))dx

    Text Solution

    |

  18. int0^1(cos^(- 1)x)^2dx

    Text Solution

    |

  19. Evaluate the following integral: int1^2x\ sqrt(3x-2)\ dx

    Text Solution

    |

  20. Evaluate the following integral: int0^1cos^(-1)x\ dx

    Text Solution

    |