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Q. $\displaystyle \lim_{x \to 0}$$\frac{\int^{x}_{0}t\,sin\left(10t\right)dt}{x}$ is equal to :

JEE MainJEE Main 2020Limits and Derivatives

Solution:

Using L.H. Rule
$\displaystyle \\lim_{x\to0} \frac{x\,sin \,\left(10x\right)}{1} = 0$