Q114 / 160 · AP EAMCET 2004 · Mathematics
$\int \frac{\sqrt{\cot x}}{\sin x \cos x} d x=-f(x)+c \Rightarrow f(x)$
- A$2 \sqrt{\tan x}$
- B$-2 \sqrt{\tan x}$
- C$-2 \sqrt{\cot x}$
- Correct answerD$2 \sqrt{\cot x}$
Solution
Given that,
$$
\begin{aligned}
& \int \frac{\sqrt{\cot x}}{\sin x \cos x} d x=-f(x)+c \\
& \Rightarrow \quad \int \frac{\sqrt{\cot x}}{\cot x \sin ^2 x} d x=-f(x)+c \\
& \Rightarrow \quad \int \frac{1}{\sqrt{\cot x \sin ^2 x}} d x=-f(x)+c \\
& \Rightarrow \quad-2 \sqrt{\cot x}+c=-f(x)+c \\
& \Rightarrow \quad f(x)=2 \sqrt{\cot x} \\
&
\end{aligned}
$$
Hence, the correct answer is option: 'D'.