A) \[3-e\]
B) \[3+e\]
C) \[5-e\]
D) \[5+e\]
Correct Answer: A
Solution :
Required Area \[=\int\limits_{1}^{e}{\left( \ell nx-{{(\ell nx)}^{2}} \right)\,\,dx}\] |
Put \[\ell nx=t\,\] \[dx={{e}^{t}}dt\] |
\[=\int\limits_{0}^{1}{(t-{{t}^{2}}){{e}^{t}}dt={{e}^{t}}\left[ \left( t-{{t}^{2}} \right)-(1-2t)+(-\,2) \right]_{0}^{1}}\] |
\[=3-e\] |
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