Mathematics

Problem

Suppose

\lim_{x \to 0} \frac{\int_{0}^{x} \frac{t^2 dt}{(a+t^r)^{1/p}}}{bx - \sin x} = l

, where

p \in \mathbb{N}, p \ge 2, a > 0, r > 0

and

b \ne 0

. If

p = 3

and

l = 1

, then the value of

a

is equal to a. 8 b. 3 c. 6 d.

3/2