Given, equation of parabola x2 = y and line y = x + 2
Solving the above equations, we get
![\[\begin{array}{*{35}{l}} {{x}^{2}}~=\text{ }x\text{ }+\text{ }2 \\ {{x}^{2}}~-\text{ }x\text{ }-\text{ }2\text{ }=\text{ }0 \\ {{x}^{2}}~-\text{ }2x\text{ }+\text{ }x\text{ }-\text{ }2\text{ }=\text{ }0 \\ x\left( x\text{ }-\text{ }2 \right)\text{ }+\text{ }1\left( x\text{ }-\text{ }2 \right)\text{ }=\text{ }0 \\ \left( x\text{ }+\text{ }1 \right)\text{ }\left( x\text{ }-\text{ }2 \right)\text{ }=\text{ }0 \\ So,\text{ }x\text{ }=\text{ }-1,\text{ }2 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-48d9ab5e946177f867275298a35e1582_l3.png "Rendered by QuickLaTeX.com")
Now,
Therefore, the area of the required region is 9/2 sq. units.
Find the area of the region enclosed by the parabola x^2 = y and the line y = x + 2
Find the area of the region enclosed by the parabola x^2 = y and the line y = x + 2