JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \([\cdot]\) denote the greatest integer function. Then \(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{12(3+[x])}{3+[\sin x]+[\cos x]}\right) d x\) is equal to:
- A \(15\pi+4\)
- B \(11\pi+2\)
- C \(13\pi+1\)
- D \(12\pi+5\)
Answer & Solution
Correct Answer
(B) \(11\pi+2\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{12(3+[x])dx}{3+[\sin x]+[\cos x]}\) \(I=\int_{-\frac{\pi}{2}}^{-1}\frac{12(1)dx}{2}+\int_{-1}^{0}\frac{12(2)dx}{2}+\int_{0}^{1}\frac{12(3)dx}{3}+\int_{1}^{\frac{\pi}{2}}\frac{12(4)dx}{3}\)…
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