# Can you find a general rule for this? - Part (1)

Calculus Level 5

If $$x,z$$ are real numbers with $$z > 0$$, there exist unique integer $$m$$ and real number $$r$$ with $$0 \le r < z$$ so that $$x = mz + r$$. Define the remainder $$\{x \text{ mod } z\}$$ as the value of $$r$$ for the corresponding $$x,z$$.

Compute $6 \int_0^1 \{x^2 \text{ mod } x\}\,dx$

×