# Area with a Twist(Corrected)

Calculus Level 5

The area bounded by $$y=f(x)$$, $$x=\frac{1}{2}$$, $$x=\frac{\sqrt{3}}{2},$$ and the $$x$$-axis is $$A$$ square units, where $f(x) = x+ \dfrac{2}{3}x^3 + \dfrac{2}{3}\cdot\dfrac{4}{5}x^5 + \dfrac{2}{3}\cdot\dfrac{4}{5}\cdot\dfrac{6}{7}x^7+ \cdots$ and $$|x| < 1.$$

If $$A$$ can be written as $$\dfrac{\pi^a}{b}$$, where $$a$$ and $$b$$ are positive integers, find $$a + b$$.

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