The curve y = –x2 or x2 = –y and the line x + y + 2 = 0
Solving the two equation, we get
![\[x\text{ }-\text{ }{{x}^{2}}~+\text{ }2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b382dd72ea0b643c954ddfeb4e595dc4_l3.png "Rendered by QuickLaTeX.com")
![\[{{x}^{2}}~\text{ }-x\text{ }\text{ }-2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-711752f50a34fc314b0db1b6929794ee_l3.png "Rendered by QuickLaTeX.com")
![\[{{x}^{2}}~\text{ }-2x\text{ }+\text{ }x\text{ }-\text{ }2\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5cfd18a6d62ad19655f2aef700782855_l3.png "Rendered by QuickLaTeX.com")
![\[x\left( x\text{ }-\text{ }2 \right)\text{ }+\text{ }1\text{ }\left( x\text{ }-\text{ }2 \right)\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ee6453c39ab313a854594462c49b63c3_l3.png "Rendered by QuickLaTeX.com")
![\[\left( x\text{ }-\text{ }2 \right)\text{ }\left( x\text{ }+\text{ }1 \right)\text{ }=\text{ }0\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6ee7248d27f752cd95f9f090cb371ad9_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }-1,\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-85928d9df538e32375824d9722eb2f20_l3.png "Rendered by QuickLaTeX.com")
The area of the required shaded region
Therefore, the required area = 9/2 sq.units
Find the area enclosed by the curve y = –x^2 and the straight-line x + y + 2 = 0.
Find the area enclosed by the curve y = –x^2 and the straight-line x + y + 2 = 0.