TS EAMCET · Maths · Definite Integration
\([\bullet]\) is the greatest integer function then \(\int_0^{2 \pi}[|\sin x+| \cos \mid] d x=\)
- A \(\frac{ \pi}{2}\)
- B \({ \pi}{2}\)
- C \(\frac{3 \pi}{2}\)
- D \(2{ \pi}\)
Answer & Solution
Correct Answer
(D) \(2{ \pi}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { (d) } \int_0^{2 \pi}[|\sin x|+|\cos x|] d x \\ & \because \quad|\sin x| \geq \sin ^2 x \\ & \quad|\cos x| \geq \cos ^2 x \\ & \therefore \quad|\sin x|+|\cos x| \geq \sin ^2 x+\cos ^2 x \\ & \quad|\sin x|+|\cos x| \geq 1 \end{aligned}\) also max. value…
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