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JEE Advanced2010MathematicsLimitsActual

The value of _ x 0 1 x^3 ₀^x t (1+t) t^4+4 d t is

Options

  1. A0
  2. B1 12
  3. C1 24
  4. D1 64

Correct answer

B. 1 12

Step-by-step solution

_ x 0 1 x^3 ₀^ x t (1+t) 4+t^4 d t Using L' Hospital's rule, aligned & = _ x 0 x (1+x) 4+x^4 3 x^2 = & _ x 0 (1+x) 3 x 1 4+x^4 = & 1 3 1 4 = 1 12 [ using, _ x 0 (1+x) x =1 ] aligned

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