LaTeX Integrals, Sums, and Limits—How to Write Them

Calculus homework lives on these three structures. The syntax isn’t hard; the traps are mostly missing braces around limits.

Sums

\sum_{i=1}^{n} a_i

Write \sum_{i=1}^{n}. If you write \sum_i=1^n, the =1 escapes the subscript and the layout looks broken immediately.

Integrals

\int_{a}^{b} f(x)\, dx
\iint_{D} f(x,y)\, dA
\oint_{C} \vec{F}\cdot d\vec{r}

\, adds a thin space before the differential. Optional, but a good habit.

Limits

\lim_{x \to 0} \frac{\sin x}{x}
\lim_{n \to \infty} a_n

\to or \rightarrow both work.

Drop a template in the LaTeX editor, fix the limits and integrand, then copy. For “parameter moves, picture moves,” pair with calculus resources—especially Riemann sums and the derivative tangent tools.