WBJEE · Maths · Indefinite Integration
Let \([x]\) denote the greatest integer less than or equal to \(x\), then the value of the integral \(\int_{-1}^{1}(|x|-2[x]) d x\) is equal to
- A 3
- B 2
- C -2
- D -3
Answer & Solution
Correct Answer
(A) 3
Step-by-step Solution
Detailed explanation
Let \(I=\int_{-1}^{1}(|x|-2[x]) d x\) \(=\int_{-1}^{0}(|x|-2[x]) d x+\int_{0}^{1}(|x|-2[x]) d x\) \(=\int_{-1}^{0}(-x-2(-1)) d x+\int_{0}^{1}(x-2(0)) d x\) \(\quad=\int_{-1}^{0}(-x+2) d x+\int_{0}^{1} x d x\)…
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