## Integral

integral

$\int_0^1 f(x) dx$

\int_0^1 f(x) dx

The symbol "\int" is derived from the concept of integration. The limits of integration are represented using a subscript and a superscript.

integral large

$\displaystyle \int_{-\infty}^{ \infty } f(x) dx$

\displaystyle \int_{-\infty}^{ \infty } f(x) dx

Adding "\displaystyle" causes the expression to be displayed in a larger format. When including multiple symbols within the integral section, they are enclosed in curly brackets.

integral sample

$\begin{eqnarray} \int_0^1 x dx = \left[ \frac{x^2}{2} \right]_0^1 = \frac{1}{2} \end{eqnarray}$

\begin{eqnarray}
\int_0^1 x dx
= \left[ \frac{x^2}{2} \right]_0^1
= \frac{1}{2}
\end{eqnarray}

Here is an example of a integral calculation:

double integral

$\iint_D f(x,y) dxdy$

\iint_D f(x,y) dxdy

By stacking the symbol "i" (integral) multiple times, such as "\iint" for double integral, "\iiint" for triple integral, and "\iiiint" for quadruple integral, we represent iterated integrals.

multiple integral

$\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n$

\idotsint_D f(x_1, x_2, \ldots , x_n) dx_1 \cdots dx_n

By combining "int", "dots", and "int" together, we get the symbol "idotsint."

contour integral

$\oint_C f(z) dz$

\oint_C f(z) dz

The symbol "oint" represents a contour integral, where the "o" attached to the "int".

Formula
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