![]() Given a function f of a real variable x, and an interval of the real line, the definite integral \int_a^b \! f(x)\,dx is defined informally to be the 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. Integration is an important concept in mathematics and-together with its inverse, differentiation-is one of the two main operations in calculus. integration: the operation of finding the region in the x-y plane bound by the function.The definite integral of f over the interval a to b is given by \int_a^b f = F\vert_a^b, where F is an anti-derivative of f.Integration is linear, additive, and preserves inequality of functions.In this case, it is called an indefinite integral and is written, \int f(x)\,dx = F(x) + C. The term integral may also refer to the notion of the anti- derivative, a function F whose derivative is the given function f. ![]()
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