Mathematics - Area Under Curves Question with Solution | TestHub

Required area $=$ Area of OAB + Area of ABC
Now, Area of $\mathrm{OAB}={\int }_0^1\mathrm{f}(\mathrm{x})\mathrm{dx}+{\int }_1^2\mathrm{g}(\mathrm{x})\mathrm{dx}$ $={\int }_0^1{x}^{2}dx+{\int }_1^2(-x+2)dx$ $={\frac{x^3}{3}|}_0^1+{\left[\frac{-x^2}{2}+2x\right]}_1^2$ $=\frac{1}{3}+\left[\left(\frac{-4}{2}+4\right)-\left(\frac{-1}{2}+2\right)\right]$ $=\frac{1}{3}+\left[(-2+4)-\left(\frac{3}{2}\right)\right]$ $=\frac{1}{3}+\frac{1}{2}=\frac{5}{6}$ sq unit