Editing Integral (section)

===Analytical===
The most basic technique for computing definite integrals of one real variable is based on the [[fundamental theorem of calculus]]. Let {{math|''f''(''x'')}} be the function of {{mvar|x}} to be integrated over a given interval {{math|[''a'', ''b'']}}. Then, find an antiderivative of {{mvar|f}}; that is, a function {{mvar|F}} such that {{math|''F''′ {{=}} ''f''}} on the interval. Provided the integrand and integral have no [[Mathematical singularity|singularities]] on the path of integration, by the fundamental theorem of calculus,

:<math>\int_a^b f(x)\,dx=F(b)-F(a).</math>

Sometimes it is necessary to use one of the many techniques that have been developed to evaluate integrals. Most of these techniques rewrite one integral as a different one which is hopefully more tractable. Techniques include [[integration by substitution]], [[integration by parts]], [[Trigonometric substitution|integration by trigonometric substitution]], and [[Partial fractions in integration|integration by partial fractions]].

Alternative methods exist to compute more complex integrals. Many [[nonelementary integral]]s can be expanded in a [[Taylor series]] and integrated term by term. Occasionally, the resulting infinite series can be summed analytically. The method of convolution using [[Meijer G-function]]s can also be used, assuming that the integrand can be written as a product of Meijer G-functions. There are also many less common ways of calculating definite integrals; for instance, [[Parseval's identity]] can be used to transform an integral over a rectangular region into an infinite sum. Occasionally, an integral can be evaluated by a trick; for an example of this, see [[Gaussian integral]].

Computations of volumes of [[solid of revolution|solids of revolution]] can usually be done with [[disk integration]] or [[shell integration]].

Specific results which have been worked out by various techniques are collected in the [[Lists of integrals|list of integrals]].