Integral Calculus Question 299
Question: If $ \int_{{}}^{{}}{\frac{f(x)\ dx}{\log \sin x}=\log \log \sin x} $ , then $ f(x)= $
Options:
A) $ \sin x $
B) $ \cos x $
C) $ \log \sin x $
D) $ \cot x $
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Answer:
Correct Answer: D
Solution:
$ \int_{{}}^{{}}{\frac{f(x),dx}{\log \sin x}}=\log \log \sin x $ Differentiating both sides, we get $ \frac{f(x)}{\log \sin x}=\frac{\cot x}{\log \sin x}\Rightarrow f(x)=\cot x. $
BETA
