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MHT CET2008MathematicsDefinite Integration

The value of ₀^ x ³ x d x is

Options

  1. A4 3
  2. B2 3
  3. C0
  4. DNone of these

Correct answer

B. 2 3

Step-by-step solution

Let I= ₀^ x ³ x d x ...(i) Also, I= ₀^ ( -x) ³ x d x ...(ii) On adding Eqs. (i) and (ii), we get aligned 2 I &= ₀^ ³ x d x &= 4 ₀^ (3 x- 3 x) d x &= 4 [-3 x+ 3 x 3 ]₀^ &= 4 [3- 1 3 +3- 1 3 ]= 4 3 Hence, I &= 2 3 aligned

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