A) \[\frac{1}{2}\]
B) \[\frac{1}{3}\]
C) \[\frac{2}{9}\]
D) \[\frac{9}{2}\]
Correct Answer: D
Solution :
Given equation of parabola can be rewritten as\[{{x}^{2}}=-(y-2)\]and equation of line is\[y=-x\]. \[\therefore \]Point of intersection are \[A(-1,\,\,1)\] and\[D(2,\,\,-2)\]. \[\therefore \]Required area\[=\int_{-1}^{2}{({{y}_{1}}-{{y}_{2}})dx}\] \[=\int_{-1}^{2}{(2-{{x}^{2}}+x)}\,dx\] \[=\left[ 2x-\frac{{{x}^{3}}}{3}+\frac{{{x}^{2}}}{2} \right]_{-1}^{2}\] \[=\left[ 4-\frac{8}{3}+2-\left( -2+\frac{1}{3}+\frac{1}{2} \right) \right]\] \[=8-\frac{8}{3}-\frac{1}{3}-\frac{1}{2}\] \[=\frac{9}{2}sq\,\,unit\]You need to login to perform this action.
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