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COMEDK2016MathematicsDefinite Integration

If I₁= ₀^ / 2 x x d x and I₂= ₀^ / 2 x x d x , then which one of the following is true?

Options

  1. AI₁=I₂
  2. BI₁+I₂=0
  3. CI₁= 2 I₂
  4. DI₁+I₂= 2

Correct answer

D. I₁+I₂= 2

Step-by-step solution

I₁- ₀^ / 2 x x d x= [-x x+ x ]₀^ / 2 =[-x x+ x]₀^ / 2 =0+ 2 -0=1 Similarly, I₂= ₀^ / 2 x x d x = [x x- _ x]₀^ / 2 . =[x x+ x]₀^ / 2 = 2 2 -1= 2 -1 Hence, I₁+I₂=1+ 2 -1= 2

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