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NDA2018MathematicsDefinite IntegrationActual

What is ₀^ 2 [x^2 ] d x equal to (where [.] is the greatest integer function)?

Options

  1. A2 -1
  2. B1- 2
  3. C2( 2 -1)
  4. D3 -1

Correct answer

A. 2 -1

Step-by-step solution

aligned & ₀^ 2 [x^2 ] dx & = ₀^1 [x^2 ] d x+ ₁^ 2 [x^2 ] dx aligned =0+ ₁^ 2 1 . dx ( [] is greatest integer function )=( x )₁^ 2 = 2 -1

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