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NDA2015MathematicsDefinite IntegrationActual

Consider the integral I_m= ₀^ 2 m x x d x , where m is a positive integer. What is I_m equal to?

Options

  1. A0
  2. B1
  3. Cm
  4. D2m

Correct answer

A. 0

Step-by-step solution

I _ m = ₀^ 2 mx x dx aligned & = ₀^ 2 m( -x) ( -x) d x aligned = ₀^ (2 m -2 m x) x d x= ₀^ - 2 mx x dx aligned & I _ m =- ₀^ 2 mx x dx & 2 I _ m =0 I _ m =0 aligned

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