Evaluate $\int_{0}^{π} sin (\frac{x}{2}) d x$ .

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Evaluate $\int_{1}^{4} \frac{2 x - 1}{x} d x$ .
Given that $f^{'} (x) = 3 cos (2 x)$ and $f (\frac{π}{4}) = 2$ , find the rule for $f (x)$ .
Find the total area enclosed between the curve $y = x^{3} - 4 x$ and the $x$ -axis.
The average value of the function $f (x) = 3 x^{2} - 2 x$ over the interval $[0, 3]$ is:
Evaluate $\int_{0}^{π /4} tan^{2} (x) d x$ .
If $\frac{d}{d x} [x 2 x + 1] = \frac{3 x + 1}{2 x + 1}$ , evaluate the exact value of $\int_{0}^{4} \frac{3 x}{2 x + 1} d x$ .