Solution:
(i)The area required is represented by the shaded area ADCBA as
![\begin{aligned} \text { Area } \mathrm{ADCBA} &=\int^{2} y d x \\ &=\int^{2} x^{2} d x \\ &=\left[\frac{x^{3}}{3}\right]_{1}^{2} \\ &=\frac{8}{3}-\frac{1}{3} \\ &=\frac{7}{3} \text { units } \end{aligned}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-79d521fa9752896f9a200d33622d0592_l3.png "Rendered by QuickLaTeX.com")
(ii). The area required is represented by the shaded area ADCBA as
![\begin{array}{l} =\left[\frac{x^{5}}{5}\right]_{1}^{5} \\ =\frac{(5)^{5}}{5}-\frac{1}{5} \\ =(5)^{4}-\frac{1}{5} \\ =625-\frac{1}{5} \\ =624.8 \text { units } \end{array}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2027660467b6a18e3b72dacf5f2a6045_l3.png "Rendered by QuickLaTeX.com")
Find the area under the given curves and given lines: (i) 
