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KCET2013MathematicsDefinite 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

Given, aligned I₁ &= ₀^ / 2 x x d x and I₂= ₀^ / 2 x x d x Now, l₁ &=[x(- x)]₀^ / 2 - ₀^ / 2 1 (- x) d x &=[0+0]+[ x]₀^ / 2 =1 and l₂ &=[x x]₀^ / 2 - ₀^ / 2 1 x d x &= [ 2 -0 ]-[- x]₀^ / 2 &= 2 +(0-1)= 2 -1 & l₁+I₂= 2 aligned

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