# Large areas!

Calculus Level 4

What is the area bounded by the curve $$y=x^6( \pi - x) ^8$$ between $$x=0$$ to $$x=\pi$$ and $$x$$-axis?

The area can be represented as $$\dfrac{ \pi ^ab! c!}{d!}$$, where $$a$$, $$b$$, $$c$$, and $$d$$ are positive integers. Find the value of $$a+b+c+d$$.

 Notation: $$!$$ is the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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