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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.

L a T e X code Output
Integral $\int_{a}^{b} x^2 dx$ inside text Integral1.png
$$\int_{a}^{b} x^2 dx$$ Integral2.png

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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.

L a T e X code Output

$\iint_V \mu(u,v) \,du\,dv$$

$$\iiint_V \mu(u,v,w) \,du\,dv\,dw$$

$$\iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw$$

$$\idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k$$

Integral3.png

$$\oint_V f(s) \,ds$$

$$\oiint_V f(s,t) \,ds\,dt$$

Integral4.png

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Sums and products

Like integral, sum expression can be added using the

\sum_{lower}^{upper} 

command.

L a T e X code Output
Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text Sum1.png
$$\sum_{n=1}^{\infty} 2^{-n} = 1$$ Sum2.png

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

\prod_{lower}^{upper} 

command.

L a T e X code Output
Product $\prod_{i=a}^{b} f(i)$ inside text Prod1.png
$$\prod_{i=a}^{b} f(i)$$ Prod2.png

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Limits

Limit expression can be added using the

\lim_{lower}

command.

L a T e X code Output
Limit $\lim_{x\to\infty} f(x)$ inside text Lim1.png
$$\lim_{x\to\infty} f(x)$$ Lim2.png

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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.

L a T e X code Output
Integral $\int_{a}^{b} x^2 dx$ inside text Integral1.png
Improved integral $\int\limits_{a}^{b} x^2 dx$ inside text Limits1.png
Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text Sum1.png
Improved sum $\sum\limits_{n=1}^{\infty} 2^{-n} = 1$ inside text Limits2.png

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