A calculus problem by Daniel Thompson

Calculus Level pending

Let F F be defined by F ( x ) = 0 x 3 ( 0 y 2 ( 0 z x 3 y 2 z t d t ) d z ) d y F(x)=\int_{0}^{x^3}\left (\int_{0}^{y^2} \left (\int_{0}^{z} x^3y^2zt \; \mathrm{d}t \right )\mathrm{d}z \right )\mathrm{d}y

F ( 2 7 ) = a b F' \left (\sqrt[7]{2}\right)=\frac{a}{b} for relatively prime positive integers a a and b b . What is the value of a + b a+b ?


The answer is 155.

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