A) \[\frac{2}{5}\]
B) \[\frac{1}{3}\]
C) \[1\]
D) \[\frac{1}{2}\]
Correct Answer: B
Solution :
Intersecting points are \[x=1,4\] \[\therefore \]Required area \[=_{\begin{smallmatrix} \int_{{}}^{{}}{{}} \\ 1 \end{smallmatrix}}^{4}\left[ 2\sqrt{x}-\left( \frac{2x+4}{3} \right) \right]dx\] \[\left. =\frac{2{{x}^{{}^{3}/{}_{2}}}}{{}^{3}/{}_{2}} \right|-\left. =\frac{2{{x}^{2}}}{3\times 2} \right|_{1}^{4}-\left. \frac{4}{3}x \right|_{1}^{4}\] \[=\frac{4}{3}\left( {{4}^{{}^{3}/{}_{2}}}-{{1}^{{}^{3}/{}_{2}}} \right)-\frac{1}{3}(16-1)-\left[ \frac{4}{3}(4)-\frac{4}{3} \right]\] \[=\frac{4}{3}(7)-5-4=\frac{28}{3}-9=\frac{28-27}{3}=\frac{1}{3}\]
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