Evaluate the definite integral $\int_{0}^{1} x e^{x} d x$ .

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Find the volume of the solid generated by revolving the region bounded by $y = x$ , $y = 0$ , and $x = 4$ about the x-axis.
What is the angle between the two vectors $u = (1, 0, 1)$ and $v = (0, 1, 1)$ ?
Evaluate $\int \frac{2 x + 3}{x ^{2} + 3 x + 5} d x$ .
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Evaluate $\int_{0}^{π /2} sin^{3} x cos x d x$ .
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