AP EAMCET · Maths · Indefinite Integration
If \(x \notin\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]\) and \(n \in \mathbb{Z}\), then \(\int \sqrt{1-\sin 2 x} d x=\)
- A \(-\cos x+\sin x+c\)
- B \(\cos x+\sin x+c\)
- C \(-\cos x-\sin x+c\)
- D \(\cos x-\sin x+c\)
Answer & Solution
Correct Answer
(B) \(\cos x+\sin x+c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \int \sqrt{1-\sin 2 x} d x=\int \sqrt{(\cos x-\sin x)^2 d x} \\ & =\int|\cos x-\sin x| d x \Rightarrow \sin x+\cos x+c\end{aligned}\)
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