Question

Find the area bounded by the curve y²=4a²(x-1)and the lines x=1and y=4a

Answer 1

$$\begin{gathered} \mathrm{Required}\mathrm{area}, \\ ={\int }_1^{4\mathrm{a}}2\mathrm{a}\sqrt{\mathrm{x}-1}\mathrm{dx} \\ =2\mathrm{a}{\left[\frac{3{\left(\mathrm{x}-1\right)}^{{\displaystyle \frac{3}{2}}}}{2}\right]}_1^{4\mathrm{a}} \\ =2\mathrm{a}\times \left[\frac{3{\left(4\mathrm{a}-1\right)}^{{\displaystyle \frac{3}{2}}}}{2}-0\right] \\ =3\mathrm{a}{\left(4\mathrm{a}-1\right)}^{\frac{3}{2}}\mathrm{square}\mathrm{unit} \end{gathered}$$