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int_0^1x(1-x)^ndx |
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Answer» Solution :`I=int_0^1x(1-X)^ndx` =`int_0^1(1-x)x^ndx` =`int(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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