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Given that ∫04x39+x2dx=a\displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a∫04x39+x2dx=a, what is the value of ⌊a⌋\lfloor a \rfloor⌊a⌋?
Details and assumptions
Greatest Integer Function: ⌊x⌋:R→Z\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}⌊x⌋:R→Z refers to the greatest integer less than or equal to xxx. For example ⌊2.3⌋=2\lfloor 2.3 \rfloor = 2⌊2.3⌋=2 and ⌊−3.4⌋=−4\lfloor -3.4 \rfloor = -4⌊−3.4⌋=−4.
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