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If I = ∫ x 5 + 1 x + 1 d x = f x + c and f 0 = 0 (where, c is the constant of integration), then

Options

  1. Af 1 > 1
  2. B0 < f 1 < 1
  3. Cf 1 = 1
  4. Df 1 > 2

Correct answer

B. 0 < f 1 < 1

Step-by-step solution

The given integral is I = &#8747; x + 1 x 4 - x 3 + x 2 - x + 1 x + 1 d x = &#8747; x 4 - x 3 + x 2 - x + 1 d x = x 5 5 - x 4 4 + x 3 3 - x 2 2 + x + c &#8756; f x = x 5 5 - x 4 4 + x 3 3 - x 2 2 + x &#8756; f 1 = 1 5 - 1 4 + 1 3 - 1 2 + 1 = 1 - 1 20 - 1 6 = 47 60 &#8658; 0 &#60; f 1 &#60; 1

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