## Tuesday, 13 August 2013

### "What is Integration" by Ajit Mishra's Online Classroom

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Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Given a function f of a real variable x and an interval [a, b] of the real line, the definite integral
$\int_a^b \! f(x)\,dx \,$
is defined informally to be the signed area of the region in the xy-plane bounded by the graph of f, the x-axis, and the vertical lines x = a and x = b, such that area above the x-axis adds to the total, and that below the x-axis subtracts from the total.
The term integral may also refer to the related notion of the antiderivative, a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written:
$F = \int f(x)\,dx.$
$\int_a^b \! f(x)\,dx = F(b) - F(a)\,$