JEE Mains · Maths · STD 12 - 7.2 definite integral
The value of the integral, \(\int_{1}^{3}\left[ x ^{2}-2 x -2\right] dx ,\) where \([x]\) denotes the greatest integer less than or equal to \(x\), is :
- A \(-\sqrt{2}-\sqrt{3}+1\)
- B \(-\sqrt{2}-\sqrt{3}-1\)
- C \(-5\)
- D \(-4\)
Answer & Solution
Correct Answer
(B) \(-\sqrt{2}-\sqrt{3}-1\)
Step-by-step Solution
Detailed explanation
\(\int_{1}^{3}\left(\left[(x-1)^{2}\right]-3\right) d x\) \(=\int_{1}^{2}\left[x^{2}\right]-3 \int_{1}^{3} d x\) \(=\int_{1}^{3} 0 \cdot d x+\int_{1}^{\sqrt{2}} 1 \cdot d x+\int_{\sqrt{2}}^{\sqrt{3}} 2 \cdot d x+\int_{\sqrt{3}}^{2} 3 \cdot d x-6\)…
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