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f-x-0-x-e-t-t-2-2-dt-show-that-0-1-f-t-dt-e-1-

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Question Number 147275 by ArielVyny last updated on 19/Jul/21
f(x)=∫_0 ^x e^(t−(t^2 /2)) dt show that ∫_0 ^1 f(t)dt=(√e)−1
f(x)=∫0xet−t22dtshowthat∫01f(t)dt=e−1
Answered by mindispower last updated on 19/Jul/21
∫_0 ^1 f(t)dt=[tf(t)]_0 ^1 −∫_0 ^1 tf′(t)dt =f(1)−∫_0 ^1 te^(t−(t^2 /2)) dt =∫_0 ^1 (1−t)e^(t−(t^2 /2)) dt=[e^(t−(t^2 /2)) ]_0 ^1 =(√e)−1
∫01f(t)dt=[tf(t)]01−∫01tf′(t)dt=f(1)−∫01tet−t22dt=∫01(1−t)et−t22dt=[et−t22]01=e−1
Commented by ArielVyny last updated on 20/Jul/21
thank sir
thanksir

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