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JEE Mains · Maths · STD 12 - 7.2 definite integral
If \([.]\) represents the greatest integer function, then the value of \(\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x\) is.............
- A \(3\)
- B \(6\)
- C \(4\)
- D \(1\)
Answer & Solution
Correct Answer
(D) \(1\)
Step-by-step Solution
Detailed explanation
\(I =\int_{0}^{\sqrt{\pi / 2}}\left(\left[ x ^{2}\right]+[-\cos x ]\right) d x\) \(=\int_{0}^{1} 0 dx +\int_{1}^{\sqrt{\pi / 2}} d x +\int_{0}^{\sqrt{\pi / 2}}(-1) d x\) \(=\sqrt{\frac{\pi}{2}}-1-\sqrt{\frac{\pi}{2}}=-1\) \(\Rightarrow| I |=1\)
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