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calcul-0-1-nt-n-1-1-t-t-n-dt-




Question Number 210133 by SANOGO last updated on 31/Jul/24
calcul  ∫_0 ^1 [nt^(n−1) (1−t)−t^n ]dt
calcul01[ntn1(1t)tn]dt
Answered by mr W last updated on 01/Aug/24
=∫_0 ^1 (nt^(n−1) −(n+1)t^n )dt  =[t^n −t^(n+1) ]_0 ^1   =1^n −1^(n+1)   =0
=01(ntn1(n+1)tn)dt=[tntn+1]01=1n1n+1=0

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