AP EAMCET · Maths · Indefinite Integration
\(\int(\sqrt{1+\sin (2 x)}) d x=\)
- A \(\cos (x)+\sin (x)+c\)
- B \(\cos (x)-\sin (x)+c\)
- C \(\sin (x)-\cos (x)+c\)
- D Can be option b or c depending on value of x
Answer & Solution
Correct Answer
(D) Can be option b or c depending on value of x
Step-by-step Solution
Detailed explanation
\begin{aligned} & (b, c) I=\int \sqrt{1+\sin 2 x} d x=\int|\sin x+\cos x| d x \\ & = \begin{cases}\int(\sin x+\cos x) d x, & \text { if } \sin x+\cos x \geq 0 \\ -\int(\sin x+\cos x) d x, & \text { if } \sin x+\cos x < 0\end{cases} \\ & \therefore \quad \int \begin{array}{ll}…
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