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Prove that ∫ x ex dx for x ∈ [0, 1] = 1

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Solving L.H.S

∫ x ex dx for x ∈ [0, 1]

First we will solve ∫ x ex dx

Using ILATE, we take

First function :- f(x) = x

Second function :- g(x) = ex

L.H.S = R.H.S

Hence, proved. 

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