The value of _ x 0 1 x^3 _0^x t , n(1+t) t^4+4 ,dt is

JEE Advanced 2010 Mathematics question

The value of is

(A)
(B)Correct
(C)
(D)

Answer: (B)

Solution

As both the integral and tend to 0, so the limit is of the form and L'Hôpital's rule applies. Differentiating the numerator by the Leibniz rule gives and the denominator gives . So the limit $=

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Question ID VK-025767