Mathematics - Definite Integration Question with Solution | TestHub

Let

$L=\underset{x\to 0}{\lim }\left\{\frac{48{\int }_0^x\left({\displaystyle \frac{t^3}{1+t^6}}\right)dt}{x^4}\right\}\to \frac{0}{0}$

Applying L'hospital rule, we get

$L=\underset{x\to 0}{\lim }\left\{\frac{\left({\displaystyle \frac{48x^3}{1+x^6}}\right)}{4x^3}\right\}$

$\Rightarrow L=\underset{x\to 0}{\lim }\left(\frac{12}{1+x^6}\right)$

$\Rightarrow L=12$