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Find the value of int0^1x(1-x)^ndx...

Find the value of `int_0^1x(1-x)^ndx`

Text Solution

Verified by Experts

The correct Answer is:
`1/((n+1)(n+2))`
`I=int_(0)^(1)(1-x)x^(n)dx` (replacing `x` by `1-x`)
`=int_(0)^(1)(x^(n)-x^(n+1))dx`
`=((x^(n+1))/(n+1)-(x^(n+2))/(n+2))_(0)^(1)`
`1/(n+1)-1/(n+2)=1/((n+1)(n+2))`
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