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NDA2014MathematicsDefinite IntegrationActual

Paragraph : Consider the integrals I ₁= _ 6 ^ 3 d x 1+ x and I ₂= _ 6 ^ 3 x d x x + x . Question : What is I ₁- I ₂ equal to?

Options

  1. A0
  2. B2 I
  3. CNone of the above

Correct answer

A. 0

Step-by-step solution

Consider the integrals I ₁= _ / 6 ^ / 3 d x 1+ x and I ₂= _ / 6 ^ / 3 x d x x + x Let aligned I ₁ & = _ / 6 ^ / 3 d x 1+ x ...(i) & = _ / 6 ^ / 3 x x + x d x & = _ / 6 ^ / 3 ( 2 -x ) ( 2 -x )+ ( 2 -x ) d x & [ ( 6 + 3 -x )= ( 2 -x ) ] & = _ / 6 ^ / 3 x x + x d x...(ii) aligned Adding (i) and (ii) we get aligned & 2 I ₁ & = _ / 6 ^ / 3 1 d x=[x]_ 6 ^ 3 = 3 - 6 = 6 & I ₁ & = 12 aligned aligned & I ₂= _ / 6 ^ / 3 x x + x d x ...(i) & I ₂= _ / 6 ^ / 3 ( 2 -x ) ( 2 -x ) + ( 2 -x ) d x & I ₂= _ / 6 ^ / 3 x x + x d x...(i

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