Integral
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 of the real line, the
definite integral 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: However, 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.