A) \[3e-2\]
B) \[e\]
C) \[e-\frac{1}{e}\]
D) \[e+\frac{1}{e}\]
Correct Answer: B
Solution :
Given equation of curve, \[y=1+{{\log }_{e}}x\] ?.(i) and straight line \[x=e\] ?..(ii) On solving Eqs. (i) and (ii), we get \[y=1+{{\log }_{e}}e=1+1=2\] So, the intersection point of both curve is \[(e,2).\] Area of \[O'AB=\int_{1}^{e}{y\,\,dx}=\int_{1}^{e}{(1+{{\log }_{e}}x)dx}\] \[=\{x+x{{\log }_{e}}\,x-x\}_{1}^{e}\] \[=[x\,\,{{\log }_{e}}x]_{1}^{e}=e{{\log }_{e}}e-0\] \[=e\]You need to login to perform this action.
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