AP EAMCET · Maths · Definite Integration
\(\int_{5 \pi}^{25 \pi}|\sin 2 x+\cos 2 x| d x=\)
- A \(20 \sqrt{2}\)
- B \(10 \sqrt{2}\)
- C \(40 \sqrt{2}\)
- D \(80 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(40 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
\( |\sin 2 x+\cos 2 x| = |\sqrt{2} (\frac{1}{\sqrt{2}}\sin 2x + \frac{1}{\sqrt{2}}\cos 2x)| = |\sqrt{2}\sin(2x+\frac{\pi}{4})| = \sqrt{2}|\sin(2x+\frac{\pi}{4})| \) Period of \( |\sin(2x+\frac{\pi}{4})| \) is \( T = \frac{\pi}{2} \). Integral over one period:…
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