Problems on Techniques of Integration

Use the Integration by Parts for definite integrals. Set

u &=&x\\
dv &=& e^{x}dx\;.


du &=& dx\\
v &=& e^{x}\;.


\begin{displaymath}\int_0^1 xe^{x} dx = [x e^{x}]_0^1 - \int_0^1 e^{x} dx \end{displaymath}


\begin{displaymath}\int_0^1 x e^{x} dx = [x e^{x}]_0^1 - [e^{x}]_0^1 = e - (e-1) = 1\;.\end{displaymath}

Detailed Answer.

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