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प्रश्न
Prove the following:
`int_0^1 xe^x dx = 1`
उत्तर
Let I = `int_0^1 xe^x dx = 1`
On integrating, take x as the first function.
I = `int_0^1 x e^x dx`
`= [x e^x]_0^1 - int_0^1 1 * e^x dx`
`= e - 0 - 1 [e^x]_0^1`
`= e - (e - 1)`
`= e - e + 1`
= 1
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