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NDA2016MathematicsDefinite IntegrationActual

What is _ -2 ^2 x d x- _ -2 ^2[x] d x equal to, where [ ] is the greatest integer function?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

aligned & _ -2 ^2 x d x- _ -2 ^2[x] d x & = [ x^2 2 ]_ -2 ^2- _ -2 ⁻¹[x] d x- _ -1 ^0[x] d x- ₀^1[x] d x- ₁^2[x] d x & = 1 2 [4-4]-(-2)-(-1)-0-(1) & =2+1-1=2 aligned

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