A) \[1+{{\log }_{e}}\left( \sqrt{2}+1 \right)\]
B) \[2{{\log }_{e}}\left( \sqrt{2}+1 \right)\]
C) \[2{{\log }_{e}}\left( \sqrt{2}+1 \right)-\sqrt{2}\]
D) \[{{\log }_{e}}\left( \sqrt{2}+1 \right)-\frac{1}{\sqrt{2}}\]
Correct Answer: C
Solution :
[c] Required area, \[A=2\int\limits_{0}^{\frac{\pi }{4}}{(\sec x-\cos x)\,dx}\] \[=2\left[ {{\log }_{e}}|\sec x+\tan x|-\sin x \right]_{0}^{\pi /4}\] \[=2{{\log }_{e}}(\sqrt{2}+1)-\sqrt{2}\]You need to login to perform this action.
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