TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{\sqrt{2} d x}{\cos x \sqrt{\sin 2 x}}=f(x)+c\), then \(f(x)=\)
- A \(2 \sqrt{\sec x}\)
- B \(\sqrt{\tan x}\)
- C \(2 \sqrt{\tan x}\)
- D \(2 \sqrt{2} \sqrt{\tan x}\)
Answer & Solution
Correct Answer
(C) \(2 \sqrt{\tan x}\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{\sqrt{2} d x}{\cos x \sqrt{\sin 2 x}}=f(x)+c\) (given) So, \(I=\int \frac{d x}{\cos x \sqrt{\sin x \cos x}}=\int \frac{\sec ^2 x d x}{\sqrt{\tan x}}\) Let \(\tan x=t^2 \Rightarrow \sec ^2 x d x=2 t d t\) So,…
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