# Bounds and Bounds

Calculus Level 4

Assume that the equation $$\displaystyle \int _{ 2 }^{ \sqrt [ 3 ]{ B } }{ \frac { { 12x }^{ 2 } }{ \sqrt { { x }^{ 3 }+1 } }\, dx=200 }$$ holds true where $$B=Q\times R$$ and $$Q$$ and $$R$$ are coprime integers. If $$\displaystyle \int _{ Q }^{ R }{ (-x+2)\, dx=52 }$$, what is the value of $$R$$?

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