JEE Mains · Maths · STD 12 - 7.2 definite integral
If \([x]\) is the greatest integer \(\leq x\), then \(\pi^{2} \int_{0}^{2}\left(\sin \frac{\pi \mathrm{x}}{2}\right)(\mathrm{x}-[\mathrm{x}])^{[\mathrm{x}]} \mathrm{d} \mathrm{x}\) is equal to :
- A \(2(\pi-1)\)
- B \(4(\pi-1)\)
- C \(4(\pi+1)\)
- D \(2(\pi+1)\)
Answer & Solution
Correct Answer
(B) \(4(\pi-1)\)
Step-by-step Solution
Detailed explanation
\(\pi^{2}\left[\int_{0}^{1} \sin \frac{\pi \mathrm{x}}{2}\, \mathrm{~d} \mathrm{x}+\int_{1}^{2} \sin \frac{\pi \mathrm{x}}{2}(\mathrm{x}-1)\, \mathrm{d} \mathrm{x}\right]\)…
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