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TS EAMCET · Maths · Definite Integration

\(\int_{-2}^2|[x]| d x\) is equal to

  1. A 1
  2. B 2
  3. C 3
  4. D 4
Verified Solution

Answer & Solution

Correct Answer

(D) 4

Step-by-step Solution

Detailed explanation

We have \(\int_{-2}^2|[x]| d x=\int_{-2}^{-1}|[x]| d x +\int_{-1}^0|[x]| d x +\int_0^1|[x]| d x+\int_1^2[[x] \mid d x\) \(=\int_{-2}^{-1}|-2| d x+\int_{-1}^0|-1| d x\) \(+\int_0^1|0| d x+\int_1^2|1| d x\) \(=2[x]_{-2}^{-1}+[x]_{-1}^0+0+[x]_1^2\) \(=2[-1+2]+[0+1]+[2-1]\)…