$\int_0^3\left(\left[x^2\right]+\left[\frac{x^2}{2}\right]\right) d x=a+b \sqrt{2}-\sqrt{3}-\sqrt{5}+c \sqrt{6}-\sqrt{7},$ where $a, b, c \in z$, then $a+b+c$ is equal to.........
$ =\int_0^1 0 d x+\int_1^{12} 1 d x+\int_{\sqrt{2}}^{\sqrt{3}} 2 d x$
$ +\int_{\sqrt{3}}^2 3 \mathrm{dx}+\int_2^{\sqrt{5}} 4 \mathrm{dx}+\int_{\sqrt{5}}^{\sqrt{6}} 5 \mathrm{dx} $
$ +\int_{\sqrt{6}}^{\sqrt{7}} 6 \mathrm{dx}+\int_{\sqrt{7}}^{\sqrt{8}} 7 \mathrm{dx}+\int_{\sqrt{8}}^3 8 \mathrm{dx} $
$ +\int_0^{\sqrt{2}} 0 \mathrm{dx}+\int_{\sqrt{2}}^2 1 \mathrm{dx} $
$ +\int_2^{\sqrt{6}} 2 \mathrm{dx}+\int_{\sqrt{6}}^{\sqrt{8}} 3 \mathrm{dx}+\int_{\sqrt{8}}^3 4 \mathrm{dx}=31-6 \sqrt{2}-\sqrt{3}-\sqrt{5} $
$ -2 \sqrt{6}-\sqrt{7} $
$ \mathrm{a}=31 \quad b=-6 \quad c=-2 $
$ \mathrm{a}+\mathrm{b}+\mathrm{c}=31-6-2=23$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.