AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c\), then \(g(x)\) is equal to
- A \(\frac{-2}{\sqrt{\cot x}}\)
- B \(\frac{-2}{\sqrt{\tan x}}\)
- C \(\frac{2}{\sqrt{\cot x}}\)
- D \(\frac{2}{\sqrt{\tan x}}\)
Answer & Solution
Correct Answer
(B) \(\frac{-2}{\sqrt{\tan x}}\)
Step-by-step Solution
Detailed explanation
Given, \(\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c\) \[ \text { Now, } \begin{aligned} \int \frac{d x}{\sqrt{\sin ^4 x \cot x}} & =\int \frac{d x}{\sin ^2 x \sqrt{\cot x}} \\ & =\int \frac{\operatorname{cosec}^2 x}{\sqrt{\cot x}} d x \end{aligned} \] Put \(\quad \cot x=t\)…
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