A) \[\frac{53}{3}\]
B) 18
C) 30
D) 16
Correct Answer: B
Solution :
\[{{y}^{2}}=2x\] \[x-y-4=0\] \[{{(x-4)}^{2}}=2x\] \[{{x}^{2}}+16-8x-2x=0\] \[{{x}^{2}}-10x+16=0\] \[x=8,2\] \[y=4,-2\] \[A=\int\limits_{-2}^{4}{\left( y+4-\frac{{{y}^{2}}}{2} \right)dy}\] \[\left. =\frac{{{y}^{2}}}{2} \right|_{-2}^{4}+4y|_{-2}^{4}-\left. \frac{{{y}^{3}}}{6} \right|_{-2}^{4}\] \[=(8-2)+4(6)-\frac{1}{6}(64+8)\] \[=6+24-12=18\]You need to login to perform this action.
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