Question

​The area of the bounded by the curve y² = x, line y = 4 and y-axis is _________________.

Answer 1

To find: area of the region bounded by the curve y² = x, line y = 4 and y-axis



The required area of the region = ${\int }_0^{4}xdy$
Thus,
$$\begin{gathered} \mathrm{Required}\mathrm{area}={\int }_0^{4}xdy \\ ={\int }_0^4{y}^{2}dy \\ ={\left(\frac{y^3}{3}\right)}_0^4 \\ =\left(\frac{4^3}{3}\right)-\left(\frac{0^3}{3}\right) \\ =\frac{64}{3} \\ \mathrm{Thus},\mathrm{Area}=\frac{64}{3}\mathrm{sq}.\mathrm{units} \end{gathered}$$


Hence, the area of the region bounded by the curve y² = x, line y = 4 and y-axis is $\underline{\frac{64}{3}\mathrm{sq}.\mathrm{units}}.$