Rabu, 30 November 2011

apa itu integral

definite integral
\int_a^b \! f(x)\,dx \,
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:
F = \int f(x)\,dx.
The integrals discussed in this article are termed definite 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 [ab], then, once an antiderivative F of ƒ is known, the definite integral of ƒ over that interval is given by
\int_a^b \! f(x)\,dx = F(b) - F(a)\,

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