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The number of continuous function f:[0,1] [0,1] such that f ( x ) < x ² for all x and ₀¹ f ( x ) d x = 1 3 is :

Options

  1. A0
  2. B1
  3. C2
  4. Dinfinite

Correct answer

A. 0

Step-by-step solution

f ( x ) is always positive for x [0,1] array c f ( x ) < x ² ₀¹ f ( x ) d x < ₀¹ x ² I < 1 3 array But it is given that I = 1 3 which is not possible

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