The graph above shows the polar curve \(r=2\theta + \cos{\theta}\) for \(0\leq \theta \leq \pi \). What is the area of the region bounded by the curve and the \(x\)-axis?

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$$ \frac{1}{2}\int \limits_a^b (r(\theta))^2   d\theta $$ $$ \frac{1}{2}\int \limits_0^\pi (2\theta+\cos{\theta})^2   d\theta$$ $$ \approx \boxed{17.456} $$