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Evaluate the following : int(0)^(oo) x...

Evaluate the following `:`
`int_(0)^(oo) x^(5) e^(-3x) dx`

Text Solution

Verified by Experts

The correct Answer is:
`(5!)/(3^(6))[ :' int_(0)^(oo) x^(n) e^(-ax) dx = ( n!)/( a^(n+1)) , `Here `n= 5,a = 3]`
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Knowledge Check

  • int_(0)^(oo) e^(-mx) x^(7) dx is

    A
    `(lfloorm)/( 7^(m))`
    B
    `(lfloor 7)/(m^(7))`
    C
    `(lfloorm)/( 7^(m+1))`
    D
    `(lfloor7)/( m^(8))`

  • int_(0)^(prop) e^(-3x)x^(4)dx= .

    A
    `(8)/(81)`
    B
    `(8)/(9)`
    C
    `(8)/(27)`
    D
    `(16)/(27)`.

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    Evaluate int_(0)^(1) x e^(-2x) dx

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