# Integration with Square Roots

Calculus Level 3

Given that $$\displaystyle \int_0^4 x^3\sqrt{9+x^2} dx = a$$, what is the value of $$\lfloor a \rfloor$$?

Details and assumptions

Greatest Integer Function: $$\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z}$$ refers to the greatest integer less than or equal to $$x$$. For example $$\lfloor 2.3 \rfloor = 2$$ and $$\lfloor -3.4 \rfloor = -4$$.

×