Mathematics - Application of Derivative Question with Solution | TestHub

Consider $\mathrm{g}(\mathrm{t})={\int }_0^{\mathrm{t}}\mathrm{f}(\mathrm{x})\mathrm{dx}$ Applying LMVT in $(0,2)$ $\frac{\mathrm{g}(2)-\mathrm{g}(0)}{2-0}={\mathrm{g}}^{\prime }(\mathrm{c});\mathrm{c}\in (0,2)\Rightarrow {\int }_0^2\mathrm{f}(\mathrm{x})\mathrm{dx}=2\mathrm{f}(\mathrm{c})\text{ for }\mathrm{c}\in (0,2)$