Integrals and Summations in LaTeX
LaTeX provides powerful commands for typesetting integrals, summations, and limits. This guide covers everything you need to know about writing these mathematical expressions in your documents.
Integrals
LaTeX offers various commands for different types of integrals:
| Type | Command | Example | Result |
|---|---|---|---|
| Indefinite integral | \int | \int f(x) \,dx | |
| Definite integral | \int_{a}^{b} | \int_{0}^{1} x^2 \,dx | |
| Double integral | \iint | \iint_D f(x,y) \,dx\,dy | |
| Triple integral | \iiint | \iiint_V f(x,y,z) \,dx\,dy\,dz | |
| Contour integral | \oint | \oint_C f(z) \,dz |
Always use \\, before differential terms (dx, dy, etc.) to add proper spacing.
Summations and Products
Summations and products are essential for series and sequence notation:
| Type | Command | Example | Result |
|---|---|---|---|
| Basic summation | \sum_{i=1}^{n} | \sum_{i=1}^{n} x_i | |
| Infinite series | \sum_{n=1}^{\infty} | \sum_{n=1}^{\infty} \frac{1}{n^2} | |
| Product notation | \prod_{i=1}^{n} | \prod_{i=1}^{n} x_i | |
| Double summation | \sum_{i=1}^{m} \sum_{j=1}^{n} | \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij} |
Limits
Limit notation is commonly used in calculus and analysis:
| Type | Command | Example | Result |
|---|---|---|---|
| Basic limit | \lim_{x \to a} | \lim_{x \to 0} \sin(x)/x | |
| Limit to infinity | \lim_{x \to \infty} | \lim_{x \to \infty} \frac{1}{x} | |
| One-sided limit (from left) | \lim_{x \to a^-} | \lim_{x \to 0^-} \frac{1}{x} | |
| One-sided limit (from right) | \lim_{x \to a^+} | \lim_{x \to 0^+} \frac{1}{x} |
Display Style vs. Inline Mode
LaTeX adjusts the size and positioning of integrals and summations based on the context:
Inline mode (between $ $):
Display mode (between \[ \]):
Use \\displaystyle to force display style in inline mode, but use it sparingly as it can disrupt line spacing.
Common Examples
Here are some common mathematical expressions combining integrals, sums, and limits:
Fourier Series:
Integration by Parts:
Double Integral in Polar Coordinates:
Remember to include \usepackage{amsmath} in your document preamble to access all these mathematical features.
Integrals and Summations in LaTeX
LaTeX provides powerful commands for typesetting integrals, summations, and limits. This guide covers everything you need to know about writing these mathematical expressions in your documents.
Integrals
LaTeX offers various commands for different types of integrals:
| Type | Command | Example | Result |
|---|---|---|---|
| Indefinite integral | \int | \int f(x) \,dx | |
| Definite integral | \int_{a}^{b} | \int_{0}^{1} x^2 \,dx | |
| Double integral | \iint | \iint_D f(x,y) \,dx\,dy | |
| Triple integral | \iiint | \iiint_V f(x,y,z) \,dx\,dy\,dz | |
| Contour integral | \oint | \oint_C f(z) \,dz |
Always use \\, before differential terms (dx, dy, etc.) to add proper spacing.
Summations and Products
Summations and products are essential for series and sequence notation:
| Type | Command | Example | Result |
|---|---|---|---|
| Basic summation | \sum_{i=1}^{n} | \sum_{i=1}^{n} x_i | |
| Infinite series | \sum_{n=1}^{\infty} | \sum_{n=1}^{\infty} \frac{1}{n^2} | |
| Product notation | \prod_{i=1}^{n} | \prod_{i=1}^{n} x_i | |
| Double summation | \sum_{i=1}^{m} \sum_{j=1}^{n} | \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij} |
Limits
Limit notation is commonly used in calculus and analysis:
| Type | Command | Example | Result |
|---|---|---|---|
| Basic limit | \lim_{x \to a} | \lim_{x \to 0} \sin(x)/x | |
| Limit to infinity | \lim_{x \to \infty} | \lim_{x \to \infty} \frac{1}{x} | |
| One-sided limit (from left) | \lim_{x \to a^-} | \lim_{x \to 0^-} \frac{1}{x} | |
| One-sided limit (from right) | \lim_{x \to a^+} | \lim_{x \to 0^+} \frac{1}{x} |
Display Style vs. Inline Mode
LaTeX adjusts the size and positioning of integrals and summations based on the context:
Inline mode (between $ $):
Display mode (between \[ \]):
Use \\displaystyle to force display style in inline mode, but use it sparingly as it can disrupt line spacing.
Common Examples
Here are some common mathematical expressions combining integrals, sums, and limits:
Fourier Series:
Integration by Parts:
Double Integral in Polar Coordinates:
Remember to include \usepackage{amsmath} in your document preamble to access all these mathematical features.