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Prove the following: int0^1 x e^x dx = 1...

Prove the following: `int_0^1 x e^x dx = 1`

Text Solution

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`int_0^1 x e^x dx = [x e^x]_0^1 - int_0^1 1xxe^x dx`
=`(1e^1-0)-(e^x)_0^1`
= `e-(e^1-e^0) = e^0 = 1`
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