JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \([\mathrm{t}]\) denote the greatest integer \(\leq \mathrm{t}\). Then the value of \(8 \cdot \int \limits_{-\frac{1}{2}}^{1}([2 x]+|x|) \,d x\) is .... .
- A \(2\)
- B \(3\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int_{-1 / 2}^{1}([2 \mathrm{x}]+|\mathrm{x}|)\, \mathrm{d} \mathrm{x}\) \(=\int_{-1 / 2}^{1}[2 x] d x+\int_{-1 / 2}^{1}|x| \,d x\) \(=0+\int_{-1 / 2}^{0}(-x) d x+\int_{0}^{1} x \,d x\)…
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