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The value of int(0)^(1)(Pi(i=1)^(n)(x+i)...

The value of `int_(0)^(1)(Pi_(i=1)^(n)(x+i))(Sigma_(j=1)^(n)(1)/(x+j))dx` is

A

`n(n!)`

B

`n!`

C

`n(n+1)!`

D

`n(n-1)!`

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Knowledge Check

  • The value of the integral int_(0)^(1) x (1-x)^(n) dx is

    A
    `(1)/(n+1) + (1)/(n+2)`
    B
    `(1)/((n+1) (n+2))`
    C
    `(1)/(n+2) - (1)/(n+1)`
    D
    `2((1)/(n+1)- (1)/(n+2))`

  • The value of the integral int_(0)^(1) x(1-x)^(n)dx , is

    A
    `(1)/(n+1)+(1)/(n+2)`
    B
    `(1)/((n+1)(n+2))`
    C
    `(1)/(n+2)-(1)/(n+1)`
    D
    `2((1)/(n+1)-(1)/(n+2))`

  • The value of Sigma_(i=1)^(n) Sigma_(j=1)^(i) underset(k=1)overset(j) =220, then the value of n equals

    A
    11
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