JEE Mains · Maths · STD 12 - 7.2 definite integral
If \([x]\) denotes the greatest integer less than or equal to \(x\), then the value of the integral \(\int_{-\pi / 2}^{\pi / 2}[[x]-\sin x] d x\) is equal to:
- A \(0\)
- B \(\pi\)
- C \(1\)
- D \(-\pi\)
Answer & Solution
Correct Answer
(D) \(-\pi\)
Step-by-step Solution
Detailed explanation
\(I=\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}([x]+[-\sin x] \quad \ldots \text { (i) }\) \(I=\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}([-x]+[\sin x] d x \ldots \text { (ii) }\) (King property)…
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