Integration is an important concept in mathematics and, together with differentiation, is one of the
two main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of
the real line, the definite integral
is defined informally to be the net signed area of
the region in the xy-plane
bounded by the graph of ƒ,
the x-axis, and the
vertical lines x = a and x = b.
The term integral may also refer to the notion of antiderivative, a function F whose derivative is the given function ƒ. In this case, it is called
an indefinite integral and
is written:
The integrals
discussed in this article are termed definite integrals. Some authors maintain a
distinction between antiderivatives and indefinite integrals.
The principles
of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century.
Through the fundamental theorem of calculus, which they independently
developed, integration is connected with differentiation: if ƒ is a continuous real-valued
function defined on a closed interval [a, b], then, once an antiderivative F of ƒ is known, the definite integral
of ƒ over that interval is given by
http://en.wikipedia.org/wiki/Integral
Integrals
of simple functions
Rational functions
These rational functions have a
non-integrable singularity at 0 for a ≤ −1.
(Cavalieri's
quadrature formula)
(Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Lists_of_integrals
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.