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AP EAMCET2003MathematicsDefinite Integration

_ -2 ^2|[x]| d x is equal to

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

D. 4

Step-by-step solution

We have _ -2 ^2|[x]| d x= _ -2 ⁻¹|[x]| d x + _ -1 ^0|[x]| d x + ₀^1|[x]| d x+ ₁^2[[x] d x= _ -2 ⁻¹|-2| d x+ _ -1 ^0|-1| d x+ ₀^1|0| d x+ ₁^2|1| d x=2[x]_ -2 ⁻¹+[x]_ -1 ^0+0+[x]₁^2=2[-1+2]+[0+1]+[2-1]=2+1+1=4

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