Since no one else has chimed in, I will convert my comment to an answer. As I had said, "most fonts are scalable, meaning that resolution scales to the available space."
The MWE below is a whole beamer slide, and can be seen to retain good resolution to very large font size.
\documentclass{beamer}
\usepackage{xcolor,graphicx}
\begin{document}
\begin{frame}
\centering \fboxsep=5pt
\scalebox{6}{\colorbox{blue}{\color{white}$\int f(x)dx$}}\bigskip\par
\scalebox{2.8}{\colorbox{blue}{\color{white}$\sin^2(x)+\cos^2(x)=1$}}
\end{frame}
\end{document}

Here is an alternative that does four (or five) things:
It makes the large equations in a roman, not sans serif, font, by renewing the \mathfamilydefault and
It set the integral in \displaystyle.
It uses an \fbox rather than \colorbox on the top equation (\fboxsep and \fboxrule are pertinent to the frame offset and thickness), and
It provides different color for frame vs. equation.
In frame 2, it allows specification of the equation height, rather than a scale factor.
Here is the MWE.
\documentclass{beamer}
\usepackage{xcolor,graphicx,scalerel}
\renewcommand\mathfamilydefault{\rmdefault}
\fboxsep=4pt \fboxrule 1pt
\begin{document}
\begin{frame}
\centering
\scalebox{5}{\color{blue!30!red}\fbox{\color{blue}$\displaystyle\int f(x)dx$}}\bigskip\par
\scalebox{2.8}{\colorbox{blue}{\color{white}$\sin^2(x)+\cos^2(x)=1$}}
\end{frame}
\begin{frame}
\centering
\scaleto{\color{blue!30!red}\fbox{\color{blue}$\displaystyle\int f(x)dx$}}{150pt}
150pt high\bigskip\par
\scaleto{\colorbox{blue}{\color{white}$\sin^2(x)+\cos^2(x)=1$}}{50pt} 50 pt
\end{frame}
\end{document}
Here is frame 1 with a scale factor applied

And here is frame 2 with a vertical height defined:

\documentclass{beamer} \usepackage{xcolor,graphicx} \begin{document} \centering \fboxsep=5pt \scalebox{6}{% \colorbox{blue}{\color{white}$\int f(x)dx$}}\bigskip\par \scalebox{2.8}{% \colorbox{blue}{\color{white}$\sin^2(x)+\cos^2(x)=1$}} \end{document}– Steven B. Segletes Nov 02 '15 at 18:37%signs, it should at least compile. (the spaces in the code generally denote a new line) – Steven B. Segletes Nov 02 '15 at 18:58