AP EAMCET · Maths · Definite Integration
\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x=\)
- A \(0\)
- B \(3(1-\cos 1)+\sin 2-\sin 1\)
- C \(3(1-\cos 1)+\cos 2-\sin 1\)
- D \(\cos 2-\sin 2\)
Answer & Solution
Correct Answer
(B) \(3(1-\cos 1)+\sin 2-\sin 1\)
Step-by-step Solution
Detailed explanation
\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x = \int_{-\frac{\pi}{2}}^{-1} \sin (x+2) d x + \int_{-1}^{0} \sin (x+1) d x + \int_{0}^{1} \sin (x) d x + \int_{1}^{\frac{\pi}{2}} \sin (x-1) d x\)…
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