JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\int_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x\) is equal to.
- A \(10(\pi+4)\)
- B \(10(\pi+2)\)
- C \(20(\pi-2)\)
- D \(20(\pi+2)\)
Answer & Solution
Correct Answer
(D) \(20(\pi+2)\)
Step-by-step Solution
Detailed explanation
\(I=\int_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x \quad ;(\) Jack property \()\) \(I=40 \int_{0}^{\pi / 2}(\sin x+\cos x)^{2} d x\) \(I=40 \int_{0}^{\pi / 2}(1+\sin 2 x) d x\) \(I=20[\pi+2]\)
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