A) \[\frac{1}{24}\]
B) \[\frac{1}{12}\]
C) \[\frac{1}{8}\]
D) \[\frac{1}{6}\]
Correct Answer: A
Solution :
Curve passes through the point\[(1,\,\,2).\] \[\therefore \] \[2=a+b+c\] ?(i) Also curve passes through the point\[(0,0)\]. \[\therefore \] \[c=0\Rightarrow a+b=2\] Now, \[{{\left. \frac{dy}{dx} \right|}_{(0,0)}}=2a(0)+b=1\] \[\therefore \] \[b=1;\,a=1\] Hence, the curve is\[y={{x}^{2}}+x={{(x+1\text{/}2)}^{2}}-1\text{/}4\] \[\therefore \] \[x=-1/2\]is point of minima. \[\therefore \] Required area \[A=\int\limits_{-1/2}^{0}{({{x}^{2}}+x-x)\,dx}\] \[=\int\limits_{-1/2}^{0}{({{x}^{2}})dx=1/24\,\text{sq}\text{.}\,\text{units}}\]You need to login to perform this action.
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