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If IK=int1^e(1nx)^kdx(k in I^+)dx(k in ...

If `I_K=int_1^e(1nx)^kdx(k in I^+)dx(k in I^+),` then find the value of `I_4dot`

Text Solution

Verified by Experts

The correct Answer is:
`9e-24`
`I_(k)=int_(1)^(e)(Inx)^(k)dx=|x(Inx)^(k)|_(1)^(e)-k int_(1)^(e)(Inx)^(k-1)dx`
or `I_(k)=e-kI_(k-1)`
or `I_(4)=e-4I_(3)`
`=e-4(e-3)(e-3)(e-2I_(1))`
`=9e-24 ( :' I_(1)=1)`
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