JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of \(\int\limits_{0}^{2\pi } {\left[ {\sin \,2x\left( {1 + \cos \,3x} \right)} \right]} \,dx\) where \([t]\) denotes the greatest integer function, is
- A \(\pi \)
- B \(-2\pi \)
- C \(2\pi \)
- D \(-\pi \)
Answer & Solution
Correct Answer
(D) \(-\pi \)
Step-by-step Solution
Detailed explanation
\({\mathrm{I}=\int_{0}^{2 \pi}[\sin 2 x(1+\cos 3 x)] \mathrm{d} x} \) \({2 l=\int_{0}^{2 \pi}([\sin 2 x(1+\cos 3 x)]+[-\sin 2 x-\sin 2 x \cos 3 x]) \mathrm{d} x} \) \({2 l=\int_{0}^{2 \pi}-d x} \) \({2 l=2 \int_{0}^{\pi}-d x} \) \({I=\int_{0}^{\pi}-d x \Rightarrow-\pi}\)
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