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99 Percentile Qs Bank for JEE MainMathematicsDefinite Integration

Evaluate ∫ a b x x d x ,   a < b

Options

  1. Aa - b
  2. Bb + a
  3. Cb - a
  4. DN o n e o f t h e s e

Correct answer

C. b - a

Step-by-step solution

Let, I = &#8747; a b x x d x We have, x x = 1 x &#62; 0 - 1 x &#60; 0 Case I : When 0 < a < b &#8658; I = &#8747; a b 1 . &#160; d x = x a b = b - a = b - a .......(i) Case II: When a < 0 < b I = &#8747; a 0 x x d x + &#8747; 0 b x x d x &#8658; I = - &#160; &#8747; a 0 1 . d x + &#8747; 0 b 1 . d x = - 0 - a + b - 0 = b + a = b - | a | .......(ii) Case III : When a < b < 0 &#8658; I = &#8747; a b - 1 . d x = - b - a = - b + a = b - a .......(iii) It is clear from (i), (ii) and (iii) we get &#8747; a b x x &#160; d

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