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If int0^oo x^(2n+1)\ e^(-x^2)\ dx=360, t...

If `int_0^oo x^(2n+1)\ e^(-x^2)\ dx=360,` then the value of `n` is___

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Verified by Experts

The correct Answer is:
6
`I=int_(0)^(oo) (x^(2))^(n).xe^(-x^(2)dx`
Put `x^(2)=t` and `x dx=dt//2`
`=1/2[-t^(n)e^(-t)]_(0)^(oo) +nint_(0)^(oo) t^(n-1)e^(-t)dt]`
`=1/2[0+nint_(0)^(oo) t^(n-1)e^(-t)dt]`
`=(n!)/2=360`
`impliesn=6`
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