QJEEM23Mafb5f: JEE Main 2023 Mathematics - Class 12 JEEM23Mafb5f Solution: lim x → 0 48 x 4 ∫ 0 x t 3 t 6 + 1   d t is equal to…

Question

Verified Solution • 2025–26 Session moderate

$lim_{x \to 0} \frac{48}{x^{4}} \int_{0}^{x} \frac{t^{3}}{t^{6} + 1} d t$ is equal to ___________.

Accepted Answer

48 \lim\limits_{x \rightarrow 0} \frac{\int_0^x \frac{t^3}{t^6+1} d t}{x^4}\left(\frac{0}{0}\right)

Applying L' Hospitals Rule

\begin{aligned}48 \lim _{x \rightarrow 0} \frac{x^3}{x^6+1} \times \frac{1}{4 x^3}\\\\\end{aligned}

= ${{48} \over 4}$ $\mathop {\lim }\limits_{x \to 0} {{1} \over {{x^6} + 1}} = 12$

QJEEM23Mafb5f: JEE Main 2023 Mathematics - Class 12 JEEM23Mafb5f Solution: lim x → 0 48 x 4 ∫ 0 x t 3 t 6 + 1 &nbsp; d t is equal to…