amsmathdisplaystylemath-mode
I have a mathematical equation
$$
K = \sum_{i \in \mathcal{V}} \left\lvert i^p - \mathbbm{1}_{\{i \in \mathcal{J}\}} \cdot k^p \right\rvert
$$
that when compiled, looks like:
Is there a way I could lengthen the absolute value verticals and to somehow not make the p power exponentials crunch the i and the k, as well as a better indicator function. Any suggestions what I could do will be greatly appreciated. Thanks!
You could place the fragment If $f(x) > g(x)$ on the interval $[a,b]$, then inside an \intertext directive. You should also insert thinspaces ahead of the dx terms in the integrals.
\documentclass[12pt]{article}
\usepackage[fleqn]{amsmath}
\usepackage[margin=1in]{geometry}
\begin{document}
\section{Definite Integration}
\begin{align*}
\int_a^b f(x)\,dx &= \lim_{n \to \infty} \sum_{k=1}^n f(x_k)\Delta x\\
\int_a^a f(x)\,dx &= 0\\
\int_a^b f(x)\,dx &= -\int_b^a f(x)\,dx\\
\int_a^b cf(x)\,dx &= c\int_a^b f(x)\,dx\\
\int_a^b \bigl(f(x) \pm g(x)\bigr)\,dx &= \int_a^b f(x)\,dx \pm \int_a^b g(x)\,dx\\
\int_a^p f(x)\,dx + \int_p^b f(x)\,dx &= \int_a^b f(x)\,dx\\
\intertext{If $f(x) > g(x)$ on the interval $[a,b]$, then}
\int_a^b f(x)\,dx &> \int_a^b g(x)\,dx
\end{align*}
\end{document}
A larger size for the exponent can be used, e.g. via \tfrac. Or the fraction expression can be written with a slash:
\documentclass{article}
\usepackage{amsmath}
\usepackage{geometry}
\begin{document}
\begin{equation}
\rho(T) =
\rho_{0}\exp\left[\left(\frac{T_{0}}{T}\right)^{\tfrac{1}{d+1}}\right]
\end{equation}
\begin{equation}
\rho(T) =
\rho_{0}\exp\left[\left(\frac{T_{0}}{T}\right)^{1/(d+1)}\right]
\end{equation}
\end{document}
Best Answer
$$for switch to math mode is not LaTeX command, instead it use\[...\]or\begin{equation*}...\end{equation*}mathtoolspackage (see MWE below)