A) \[\frac{8}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{2}{3}\]
D) \[\frac{4}{3}\]
Correct Answer: D
Solution :
Given equation of parabola is \[y={{x}^{2}}-x+2\] or \[{{\left( x-\frac{1}{2} \right)}^{2}}=y-\frac{7}{4}\] and equation of line is \[y=x+2\] \[\therefore \] Required area \[=\int_{0}^{2}{[x+2)-({{x}^{2}}-x+2)]dx}\] \[=\int_{0}^{2}{(-{{x}^{2}}+2x)dx}\] \[=\left[ -\frac{{{x}^{3}}}{3}+{{x}^{2}} \right]_{0}^{2}=-\frac{8}{3}+4\] \[=\frac{4}{3}sq\]unitYou need to login to perform this action.
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