Home
Class 12
MATHS
If inte^x tf (t) dt = sin x - x cos x - ...

If `int_e^x tf (t) dt = sin x - x cos x - (x^2)/2` for all `x in R - [0]`, then the value of `f(pi/6)` is :

A

`-1/2`

B

`0`

C

`2`

D

`3/2`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS (LEVEL - II)|42 Videos

  • DEFINITE INTEGRALS

    MODERN PUBLICATION|Exercise LATEST QUESTIONS FROM AIEEE/JEE EXAMINATION|13 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise Questions from karnataka CET & COMED|15 Videos

  • DETERMINANTS

    MODERN PUBLICATION|Exercise Recent competitive Questions|10 Videos

Similar Questions

Explore conceptually related problems

If int_0^x f(t) dt = x + int_x^l tf (t) dt , then the value of f(1) is :

If phi (x) = cos x - int_0^(x) (x-t) phi (t) dt , then the value of phi^('')(x) + phi (x) =

If int_(sin x)^(1) t^2 f(t) dt = 1 - sin x , then the value of f(1/(sqrt3)) is :

int_0^(4/pi) (3x^(2) sin (1/x) - x cos (1/x)dx =

int_0^(pi/2) x sin^(2) x. cos^(2) x dx =

int_0^(pi//2) cos x e^(sin x) dx is :

If f(x) = |(sin x + sin 2x + sin 3x, sin 2x , sin 3x),(3 + 4 sin x, 3, 4 sin x),(1 + sin x, sin x, 1)| then the value of int_0^(-pi//2) f(x) dx equals :

int_0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

Let T > 0 be a fixed real number. Suppose f is a continuous function such that for all x in R f(x + T) = f(x) . If I = int_6^T f(x) dx , then the value of int_(3)^(3 + 3T) f(2x)dx is:

MODERN PUBLICATION-DEFINITE INTEGRALS-RECENT COMPETITIVE QUESTIONS
  1. If inte^x tf (t) dt = sin x - x cos x - (x^2)/2 for all x in R - [0], ...

    Text Solution

    |

  2. The value of the integral int0^(pi//2) (sin^(100) x - cos^(100) x) dx ...

    Text Solution

    |

  3. If [x] denote the greatest integer function , then , int(0)^(pi//6) (1...

    Text Solution

    |

  4. If [x] denotes the greatest integer function, then : ""(2)^(4)([x] -...

    Text Solution

    |

  5. int1^(e^(17//2)) (cos(pi log x))/(x) dx =

    Text Solution

    |

  6. int0^1 x(1 - x)^(3//2) dx =

    Text Solution

    |

  7. int0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

    Text Solution

    |

  8. int0^1 (x^4 + 2x^2 + 1)d(x^2 + 1) =

    Text Solution

    |

  9. If I(1)= int(0)^(pi//2) x sin x dx and I(2)=int(0)^(pi//2) x cos x dx,...

    Text Solution

    |

  10. The value of int(-1)^(2) (|x|)/(x) dx is :

    Text Solution

    |

  11. int0^pi (cos^4 x)/(cos^4 x + sin^4 x) dx =

    Text Solution

    |

  12. If f(x) = f(pi + e - x) and inte^(pi) f(x) dx = 2/(e + pi), then inte^...

    Text Solution

    |

  13. The value of the integral int(-pi//4)^(pi//4)log(sec theta-tan theta...

    Text Solution

    |

  14. The interval I such that int0^1 (dx)/(sqrt(1 + x^4)) in I is given by ...

    Text Solution

    |

  15. int0^(pi//2) log(tan x)dx =

    Text Solution

    |

  16. The value of int(-2)^(2)(ax^(3)+bx+c) dx depends on the

    Text Solution

    |

  17. int(0)^(pi//4)log ((sin x +cos x )/(cosx))dx is equal to

    Text Solution

    |

  18. int(-pi//4)^(pi//4)(dx)/(1+cos 2x) is equal to

    Text Solution

    |

  19. int(-1)^(1) (x^(27) cos x + e^x) dx =

    Text Solution

    |

  20. The value of the integral int0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n...

    Text Solution

    |

  21. If int0^(pi) x f (sin x) dx = A int0^(pi//2) f (sin x) dx, then A is :

    Text Solution

    |