QJEEM20Ma51b7: JEE Main 2020 Mathematics - Class 12 JEEM20Ma51b7 Solution: lim x → 0 ⁡ ∫ 0 x t sin ⁡ ( 10 t ) d t x is equal to

Question

Verified Solution • 2025–26 Session moderate

lim_{x \to 0} \frac{\int_{0}^{x} t \sin (10 t) d t}{x}

is equal to

Accepted Answer

lim_{x \to 0} \frac{\int_{0}^{x} t \sin (10 t) d t}{x}

This is in

\frac{0}{0}

form.

So apply newton leibniz rule

lim_{x \to 0} \frac{x . \sin (10 x) - 0}{1}

= 0

Step-by-Step Verified Solution