Mathematics - Area Under Curves Question with Solution | TestHub

The equation of parabola $x^2=y-1$ The equation of tangent at (2,5) to parabola is $y-5={\left(\frac{dy}{dx}\right)}_{(2,5)}(x-2)$ $y-5=4(x-2)$ $4x-y=3$ Then, the required area $={\int }_0^2\left\{\left(x^2+1\right)-(4x-3)\right\}dx-$ Area of $\Delta AOD$ $={\int }_0^2\left(x^2-4x+4\right)dx-\frac{1}{2}\times \frac{3}{4}\times 3$ $={\left[\frac{(x-2{)}^3}{3}\right]}_0^2-\frac{9}{8}=\frac{37}{24}$