Mathematics - Definite Integration Question with Solution | TestHub

$\begin{array}{rl}& {\int }_0^3\left[x^2\right]dx+{\int }_0^3\left[\frac{x^2}{2}\right]dx\\ & ={\int }_0^{1}0dx+{\int }_1^{12}1dx+{\int }_{\sqrt{2}}^{\sqrt{3}}2dx\end{array}$ $\begin{array}{rl}& +{\int }_{\sqrt{3}}^{2}3\mathrm{dx}+{\int }_2^{\sqrt{5}}4\mathrm{dx}+{\int }_{\sqrt{5}}^{\sqrt{6}}5\mathrm{dx}\\ & +{\int }_{\sqrt{6}}^{\sqrt{7}}6\mathrm{dx}+{\int }_{\sqrt{7}}^{\sqrt{8}}7\mathrm{dx}+{\int }_{\sqrt{8}}^{3}8\mathrm{dx}\\ & +{\int }_0^{\sqrt{2}}0\mathrm{dx}+{\int }_{\sqrt{2}}^{2}1\mathrm{dx}\\ & +{\int }_2^{\sqrt{6}}2\mathrm{dx}+{\int }_{\sqrt{6}}^{\sqrt{8}}3\mathrm{dx}+{\int }_{\sqrt{8}}^{3}4\mathrm{dx}=31-6\sqrt{2}-\sqrt{3}-\sqrt{5}\\ & -2\sqrt{6}-\sqrt{7}\\ & \mathrm{a}=31\mathrm{b}=-6\mathrm{c}=-2\\ & \mathrm{a}+\mathrm{b}+\mathrm{c}=31-6-2=23\end{array}$