Evaluate $\int_{1}^{4} \frac{2 x - 1}{x} d x$ .

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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:
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Evaluate int 1 4 (2x - 1)/(sqrt(x)),dx. | Victorian VCE