Integrals, sums and limits

Integrals

Integral expression can be added using the

\int_{lower}^{upper} 

command.

Note, that integral expression may seems a little different in inline and display math mode - in inline mode the integral symbol and the limits are compressed.

LaTeX code	Output
Integral $\int_{a}^{b} x^2 dx$ inside text
$$\int_{a}^{b} x^2 dx$$

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Multiple integrals

To obtain double/triple/multiple integrals and cyclic integrals you must use amsmath and esint (for cyclic integrals) packages.

LaTeX code	Output
$\iint_V \mu(u,v) \,du\,dv$$ $$\iiint_V \mu(u,v,w) \,du\,dv\,dw$$ $$\iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw$$ $$\idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k$$
$$\oint_V f(s) \,ds$$ $$\oiint_V f(s,t) \,ds\,dt$$

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Sums and products

Like integral, sum expression can be added using the

\sum_{lower}^{upper} 

command.

LaTeX code	Output
Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text
$$\sum_{n=1}^{\infty} 2^{-n} = 1$$

In similar way you can obtain expression with product of a sequence of factors using the

\prod_{lower}^{upper} 

command.

LaTeX code	Output
Product $\prod_{i=a}^{b} f(i)$ inside text
$$\prod_{i=a}^{b} f(i)$$

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Limits

Limit expression can be added using the

\lim_{lower}

command.

LaTeX code	Output
Limit $\lim_{x\to\infty} f(x)$ inside text
$$\lim_{x\to\infty} f(x)$$

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Integer and sum limits improvement

In inline math mode the integral/sum/product lower and upper limits are placed right of integral symbol. Similar is for limit expressions. If you want the limits of an integral/sum/product to be specified above and below the symbol in inline math mode, use the \limits command before limits specification.

LaTeX code	Output
Integral $\int_{a}^{b} x^2 dx$ inside text
Improved integral $\int\limits_{a}^{b} x^2 dx$ inside text
Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text
Improved sum $\sum\limits_{n=1}^{\infty} 2^{-n} = 1$ inside text

Moreover, adding \displaystyle beforehand will make the symbol large and easier to read.

On the other hand, \mathlarger command (provided by relsize package) is used to get bigger integral symbol in display.

$\int\frac{1}{2}dx - \mathlarger{ \int\frac{1}{2}dx}$

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Further reading

For more information see

• Mathematical expressions
• Subscripts and superscripts
• Fractions and Binomials
• Display style in math mode