A
definite integral of a function can be represented as the signed area of the
region bounded by its graph.
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:
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
(Our solved example in mathguru.com uses this concept)
http://en.wikipedia.org/wiki/Integral
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.
(Our solved example in mathguru.com uses the below concept. This
is our own explanation, it is not taken from Wikipedia.)
=(Property of definite integrals)
Proof : Put a - x = t
-dx = dt
When x = 0, t = a
x = a, t = 0
= LHS