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Question Number 209228 by universe last updated on 04/Jul/24

Answered by Frix last updated on 04/Jul/24

∫_0 ^(π/2) (cos x +sin x)^n dx=(√2)∫_0 ^(π/2) sin^n  (x+(π/4)) dx=  =(√2)∫_(π/4) ^((3π)/4) sin^n  t dt=a∈R^+   a×lim_(n→∞)  ((√n)/2^(n/2) ) =a×0=0

π20(cosx+sinx)ndx=2π20sinn(x+π4)dx==23π4π4sinntdt=aR+a×limnn2n2=a×0=0

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