MHT CET · Maths · Indefinite Integration
\(\int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} \mathrm{~d} x=\)
- A \(2 \sqrt{\sec x}+c\), where \(c\) is a constant of integration
- B \(2 \sqrt{\tan x}+c\), where \(c\) is a constant of integration
- C \(\frac{2}{\sqrt{\tan x}}+c\), where \(c\) is a constant of integration
- D \(\frac{2}{\sqrt{\sec x}}+c\), where \(c\) is a constant of integration
Answer & Solution
Correct Answer
(B) \(2 \sqrt{\tan x}+c\), where \(c\) is a constant of integration
Step-by-step Solution
Detailed explanation
\( \int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} \mathrm{~d} x = \int \frac{\sqrt{\tan x}}{(\sin x / \cos x) \cdot \cos^2 x} \mathrm{~d} x \) \( = \int \frac{1}{\sqrt{\tan x}} \cdot \frac{1}{\cos^2 x} \mathrm{~d} x = \int (\tan x)^{-1/2} \sec^2 x \mathrm{~d} x \)
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