First slide

Evaluation of definite integrals

Question

$\int_{0}^{1} \frac{x e^{x}}{{(x + 1)}^{2}} d x$

Moderate

A

$\frac{e}{2}$
B

$\frac{e - 1}{2}$
C

$\frac{e}{2} - 1$
D

$\frac{e - 3}{2}$

Solution

$\begin{array}{l} G. I = \int_{0}^{1} [\frac{(x + 1) - 1}{(x + 1)^{2}}] e^{x} d x = \int_{0}^{1} [\frac{1}{x + 1} - \frac{1}{(x + 1)^{2}}] e^{x} d x \\ = {[\frac{e^{x}}{x + 1}]}_{0}^{1} = \frac{e}{2} - 1 \end{array}$

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