A) \[\frac{9}{8}\]
B) \[\frac{3}{4}\]
C) \[\frac{5}{4}\]
D) \[\frac{7}{8}\]
Correct Answer: A
Solution :
Given equation of parabola is \[{{x}^{2}}=4y\]and equation of straight line is \[x=4y-2.\] \[\therefore \]\[{{x}^{2}}=x+2\] \[\Rightarrow \]\[{{x}^{2}}-x-2=0\] \[\Rightarrow \]\[x=2,-1\] So, required area \[=\int\limits_{-1}^{2}{\left( \frac{x+2}{4}-\frac{{{x}^{2}}}{4} \right)dx}\] \[=\frac{1}{4}\int\limits_{-1}^{2}{\left( x+2-{{x}^{2}} \right)dx}\] \[=\frac{1}{4}\left[ \frac{{{x}^{2}}}{2}+2x-\frac{{{x}^{3}}}{3} \right]_{-1}^{2}=\frac{9}{8}sq.\]unitsYou need to login to perform this action.
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