Integral

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The integral is a generalization of area. The integral of a function is defined as the area between it and the $x$-axis. If the function lies below the $x$-axis, then the area is negative. It is also defined as the antiderivative of a function.

Basic integrals

$\int x^n =\dfrac{x^{n+1}}{n+1}$

$\int_{a}^{b} f'(x)= f(b)-f(a)$


Properties of integrals

$\int_{a}^b f = \int_a^c f + \int_c^b f$


Other uses

The word integral is the adjectival form of the noun "integer." Thus, $3$ is integral while $\pi$ is not.

The word integral is also used in English to describe the state of being integrated; e.g., "The engine is an integral part of the vehicle -- without it, nothing would work."

See also

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