Home
Class 12
MATHS
If n in N and I(n) = int (log x)^(n) dx ...

If `n in N` and `I_(n) = int (log x)^(n)` dx , then `I_(n) + n I_(n - 1) `=

A

`((log x)^(n))/(n)`

B

`((log x)^(n+1))/(n+1)`

C

`x (log x )^(n) + C`

D

`(log x)^(n - 1)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • KARNATAKA CET 2010

    KCET PREVIOUS YEAR PAPERS|Exercise Mathematics|60 Videos
  • KARNATAKA CET 2013

    KCET PREVIOUS YEAR PAPERS|Exercise Mathematics|60 Videos

Similar Questions

Explore conceptually related problems

If n in N and I_(n) = int(log x)^(n) dx , then I_(n)+nI_(n-1) =

If n in N and I_(n) = intcos^(n) xdx then nI_(n) - cos^(n-1)x. sinx =

If n(ne 1) in N and I_(n) = int tan^(n) x dx then I_(n)+I_(n-2) =

If I_(n) = int x^(n)e^(x) dx where n inN , then I_(n) + nI_(n-1) =

If n in N and I_(n) = intsin^(n) x dx then nI_(n)-(n-1)I_(n-2) =

If n(ne 1) in N and I_(n) = int e^(x)/x^(n) dx then I_(n)+ e^(x)/((n-1)x^(n-1))

If n(ne 1) in N and I_(n) =int sec^(n)x dx then (n-1) I_(n)-(n-2)I_(n-2) =

If n(ne 1) in N and I_(n) = intcot^(n) x dx then I_(n) + (cot^(n-1)x)/(n-1)

If I_(n) = int_0^(pi/4) tan^(n)x dx , then n(I_(n-1)+I_(n+1)) =

If I_(n) = int_0^(pi/2) sin^(n)x dx then I_(n)/(I_(n-2)) =

KCET PREVIOUS YEAR PAPERS-KARNATAKA CET 2012-MATHEMATICS
  1. The maximum value of x e^(-x) is

    Text Solution

    |

  2. If [x] is the greatest integer function not greater than x , then int(...

    Text Solution

    |

  3. If n in N and I(n) = int (log x)^(n) dx , then I(n) + n I(n - 1) =

    Text Solution

    |

  4. Solution of e^((dy)/(dx)) = x when x = 1 and y = 0 is

    Text Solution

    |

  5. If f(x) = {{:( (x^(2) - (a + 2) x + a)/(x - 2) " , " x ne 2) , (2 " ...

    Text Solution

    |

  6. If log(2) (9^(x - 1) + 7) - log(2) (3^(x-1) + 1) = 2 , then values of ...

    Text Solution

    |

  7. If x - 1 is a factor of x^(5) - 4x^(3) +2 x^(2) - 3x + k = 0 then k is

    Text Solution

    |

  8. If A and B have n elements in common , then the number of elements com...

    Text Solution

    |

  9. The 13^(th) term in the expansion of (x^(2) + (2)/(x))^(n) is independ...

    Text Solution

    |

  10. If one of the slopes of the pair of the lines ax^(2) + 2 hxy + by^(2) ...

    Text Solution

    |

  11. If f (x) = |{:( sin x , cos x , tan x) , (x^(3) , x^(2) , x) , (2x , 1...

    Text Solution

    |

  12. The number of solutions of equation z^(2) + barz = 0 , where z in C ar...

    Text Solution

    |

  13. The least and the greatest distances of the point (10 , 7) from the ci...

    Text Solution

    |

  14. If a-= b (mod m) and x is an integer , then which of the following is ...

    Text Solution

    |

  15. Inverse of a diagonal non-singular matrix is

    Text Solution

    |

  16. If ax^(4) + bx^(3) + cx^(2) + dx + e = |{:(x^(3) + 3x , x - 1 , x+ 3) ...

    Text Solution

    |

  17. If veca , vecb and vecc are three non-coplanar vectors and vecp , vecq...

    Text Solution

    |

  18. If (veca xx vecb)^(2) + (veca * vecb)^(2) = 144 and |veca| = 4 , then ...

    Text Solution

    |

  19. Which of the following is false ?

    Text Solution

    |

  20. 2 cos^(-1) x = sin^(-1) (2x sqrt(1 - x^(2))) is valid for all values o...

    Text Solution

    |