\[\int_{\pi \text{/4}}^{\pi \text{/2}}{{{e}^{x}}(\log \sin x+\cot x)\,dx=}\] [AI CBSE 1991]

\[-\frac{1}{2}{{e}^{\pi /4}}\log 2\]

\[\frac{1}{2}{{e}^{\pi /4}}\log 2\]

\[\int_{\pi \text{/4}}^{\pi \text{/2}}{{{e}^{x}}(\log \sin x+\cot x)

1.	\[\int_{\pi \text{/4}}^{\pi \text{/2}}{{{e}^{x}}(\log \sin x+\cot x)\,dx=}\] [AI CBSE 1991]
A.	\[{{e}^{\pi /4}}\log 2\]
B.	\[-{{e}^{\pi /4}}\log 2\]
C.	\[\frac{1}{2}{{e}^{\pi /4}}\log 2\]
D.	\[-\frac{1}{2}{{e}^{\pi /4}}\log 2\]
Answer» D. \[-\frac{1}{2}{{e}^{\pi /4}}\log 2\]

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\[\int_{\pi \text{/4}}^{\pi \text{/2}}{{{e}^{x}}(\log \sin x+\cot x)\,dx=}\] [AI CBSE 1991]

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