# A calculus problem by Akeel Howell

Calculus Level 5

Let $$f: \mathbb{R} \mapsto \mathbb{C}$$ be defined as $$\displaystyle{ f(x) = \int{\pi e^{2\arcsin(x)}}dx} \space$$ and $$f(0) = \dfrac{2\pi}{5}$$.

Find $$|f(3)|$$.

If your answer is of the form $$\dfrac{\sqrt{b}}{a}\pi e^{\pi}$$, where $$a$$ and $$b$$ are prime numbers, find $$a+b$$.

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