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  4. lim x arrow 0 (1/x)[∫ya e sin 2 t d t-∫x+ya e sin 2 t d t] is equal to

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Q. $\lim _{x \rightarrow 0} \frac{1}{x}\left[\int_{y}^{a} e^{\sin ^{2} t} d t-\int_{x+y}^{a} e^{\sin ^{2} t} d t\right]$ is equal to

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Solution:

$e^{sin^2\, y}$