\documentclass[]{article}
\title{Integrals, Sums and Limits}
\usepackage{esint}
\usepackage{amsmath}
\date{}
\author{Rakshit Rabugotra}

\begin{document}
\maketitle

\section{Integrals}
Integral \(\int_{a}^{b} x^2 \,dx\) inside text. ~\\
The same integral on display:
\[int_{a}^{b} x^2 \,dx\]
and multiple integrals:
\begin{gather*}
    \iint_V \mu(u, v) \,du\,dv
    \\
    \iiint_V \mu(u, v, w) \,du\,dv\,dw
    \\
    \oint_V f(s) \,ds
\end{gather*}


\section{Sums and products}
Sum \(\sum_{n=1}^{\infty} 2^{-n} = 1\) inside text.~\\
The same sum on display:
\[\sum_{n=1}^{\infty} 2^{-n} = 1\]

Product \(\prod_{i=a}^{b} f(i)\) inside text.
The same product on display:
\[\prod_{i=a}^{b} f(i)\]

\section{Limits}
Limit \(\lim_{x\to\infty} f(x)\) inside text.~\\
The same limit on display:
\[\lim_{x\to\infty} f(x)\]

\end{document}