$\lim _{\mathrm{x} \rightarrow 0} \frac{\int_{0}^{\mathrm{x}} \mathrm{t} \sin (10 \mathrm{t}) \mathrm{dt}}{\mathrm{x}}$ is equal to:

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Limits

lim_{x \to 0} \frac{\int _{0}^{x} t s i n ( 10 t ) dt}{x}

is equal to:

Answer: (A)

x \to 0

both the integral in the numerator and the denominator tend to

0

, so apply L'Hopital's rule; differentiating the numerator by the fundamental theorem of calculus gives

x sin (10 x)

while the denominator gives

1

. Hence the limit is

x \to 0 lim \frac{x sin ( 10 x )}{1} = 0

JEE Main · 2020 · 08 Jan 2020 · Shift 2 · Single correct option

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