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TS EAMCET · Maths · Indefinite Integration

For \(x \in\left(\frac{3 \pi}{4}, \pi\right), \int(\sqrt{1+\sin 2 x}+\sqrt{1-\sin 2 x})\) \(d x=\)

  1. A \(-2 \cos x+C\)
  2. B \(2 \sin x+C\)
  3. C \(-2 \sin x+c\)
  4. D \(2 \cos x+C\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(-2 \cos x+C\)

Step-by-step Solution

Detailed explanation

\(\left.\int(\sqrt{1+\sin 2 x})+\sqrt{1-\sin 2 x}\right) d x\) \(=\int\left(\sqrt{\sin ^2 x+\cos ^2 x+2 \sin x \cos x}\right.\) \(+\sqrt{\left.\sin ^2 x+\cos ^2 x-2 \sin x \cos x\right)} d x\) \(=\int((\sin x+\cos x)+(\sin x-\cos x)) d x\)…