A) \[\frac{3}{2}\]sq units
B) \[\frac{9}{3}\]sq units
C) \[\frac{9}{2}\]sq units
D) None of these
Correct Answer: C
Solution :
Given curve \[y=2x-{{x}^{2}}\] \[\Rightarrow \] \[{{(x-1)}^{2}}=-(y-1)\] and line \[y=-x\]. The point of intersection are (0, 0) and\[(-3,3)\]. \[\therefore \]Required area\[=\int_{0}^{3}{[(2x-{{x}^{2}})-(-x)]}\,dx\] \[=\int_{0}^{3}{(3x-{{x}^{2}})}\,dx\] \[=\left( \frac{3{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3} \right)_{0}^{3}\] \[=\frac{9}{2}\]sq unitsYou need to login to perform this action.
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