Home
Class 12
MATHS
Prove that int0^(102)(x-1)(x-2)(x-100) ...

Prove that `int_0^(102)(x-1)(x-2)(x-100)` `x(1/((x-1)+1/((x-2))+1/((x-100))dx=101 !-100 !`

Text Solution

Verified by Experts

The correct Answer is:
NA
`I=int_(0)^(102)(x-1)(x-2)……(x-100)`
`xx(1/((x-1))+1/((x-2))+…+1/((x-100)))dx`
`-int_(0)^(102)d/(dx)((x-1)(x-2)………(x-100))dx`
`=[(x-1)(x-2)…………(x-100)]_(0)^(102)`
`=101!-100!`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise SCQ_TYPE|113 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLE_TYPE|20 Videos

  • CURVE TRACING

    CENGAGE ENGLISH|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

Prove that int_0^(102)(x-1)(x-2)..(x-100)xx(1/(x-1)+1/(x-2) +.... .+ 1/(x-100))dx=101 !-100 !

Prove that int_0^1x e^x dx=1

int_(0)^(1) (1)/(x^(2)+x+1)dx

Prove that int_0^1 tan^-1((2x-1)/(1+x-x^2))dx=0

int_0^1 (x/(x+1))dx

int_0^2||x-1|-x|dx

int_0^1 x(1-x)^(5/2) dx

int_0^1cot^(- 1)(1-x+x^2)dx

Prove that: int_(0)^(oo) (x)/((1+x)(1+x^(2)))dx =(pi)/(4)

int_(0)^(1) (1)/(1+x+2x^(2))dx

CENGAGE ENGLISH-DEFINITE INTEGRATION -CAE_TYPE
  1. Evaluate: int(pi//6)^(pi//4)(1+cotx)/(e^(x)sinx) dx

    Text Solution

    |

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

    Text Solution

    |

  3. Prove that int0^(102)(x-1)(x-2)(x-100) x(1/((x-1)+1/((x-2))+1/((x-100...

    Text Solution

    |

  4. Show that : int0^1(logx)/((1+x))dx=-int0^1(log(1+x))/x dx

    Text Solution

    |

  5. If int0^1(e^t)/(1+t)dt=a , then find the value of int0^1(e^t)/((1+t)^2...

    Text Solution

    |

  6. Let f be a one to one continuous function such that f(2)=3 and f(5)=6....

    Text Solution

    |

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

    Text Solution

    |

  8. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

    Text Solution

    |

  9. Evaluate ("lim")(nvecoo)sum(k=1)^nk/(n^2+k^2)

    Text Solution

    |

  10. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

    Text Solution

    |

  11. Evaluate the following limit: lim(nto oo)[(n!)/(n^(n))]^(1//n)

    Text Solution

    |

  12. P rov et h a t4lt=int1^3sqrt(3+x^2)lt=4sqrt(3)

    Text Solution

    |

  13. If I1=int0^1 2^x^2,I2=int0^1 2^x^3dx ,I3=int1^2^x^2dx ,I4=int1^2 2^x^3...

    Text Solution

    |

  14. IfII=int0^(pi//2)cos(sinx)dx ,I2=int0^(pi/2)sin(cosx)d ,a n dI3=int0^(...

    Text Solution

    |

  15. Prove that pi/6<int0^1(dx)/(sqrt(4-x^2-x^3))<pi/(4sqrt(2))

    Text Solution

    |

  16. Evaluate int(0)^(pi//2)|sinx-cosx|dx.

    Text Solution

    |

  17. Evaluate: int(-1)^4f(x)dx=4a n dint2^4(3-f(x))dx=7, then find the val...

    Text Solution

    |

  18. Evaluate int(1)^(5)sqrt(x-2)sqrt(x-1)dx.

    Text Solution

    |

  19. Evaluate: int(-1)^3(tan^(-1)(x/(x^2+1))+tan^(-1)((x^2+1)/x))dx

    Text Solution

    |

  20. Evaluate int(1)^(a)x.a^(-[log(e)x])dx,(agt1).Here [.] represents the g...

    Text Solution

    |