A) \[\sqrt{e}+1\]
B) \[\sqrt{e}-1\]
C) \[\frac{\sqrt{e}+1}{e}\]
D) \[\frac{\sqrt{e}-1}{e}\]
Correct Answer: D
Solution :
Put \[t=-\frac{1}{x}\Rightarrow dt=\frac{1}{{{x}^{2}}}dx\], then it reduces to \[\int_{-1}^{-1/2}{{{e}^{t}}dt=[{{e}^{t}}]_{-1}^{-1/2}={{e}^{-1/2}}-{{e}^{-1}}}=\frac{\sqrt{e}-1}{e}\].You need to login to perform this action.
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