integral

Constituting a whole together with other parts or factors; not omittable or removable.

• Ceasing to do evil, and doing good, are the two great integral parts that complete this duty.
• When the verdict comes down, the transformation of the wunderkind founder of Theranos from black-clad genius to besuited milquetoast will be an integral part of the story.

Of, pertaining to, or being an integer.

Relating to integration (“the process of finding the integral [noun] of a function”).

Being the root of some monic polynomial in A.

Whole; undamaged.obsolete

• A local motion keepeth bodies integral.

One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a

• The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!

One of the two fundamental operations of calculus (the other being differentiation), whereby a function's displacement, area, volume, or other qualities arising from the study of infinitesimal change are quantified, usually defined as a limiting process on a sequence of partial sums. Denoted using a; Any of several analytic formalizations of this operation: the Riemann integral, the Lebesgue integral, etc.specifically

A definite integral: the result of the application of such an operation onto a function and a suitable subset of the function's domain: either a number or positive or negative infinity. In the former case, the integral is said to be finite or to converge; in the latter, the integral is said to diver

• The integral of #92;frac#123;1#125;#123;x#125; on #91;#92;frac#123;1#125;#123;2#125;,1#93; is #92;ln(2), but the integral of the same function on (0,1#93; diverges. In notation, #92;int#95;#92;frac#123;1#125;#123;2#125;¹#92;frac#123;1#125;#
• Stokes' theorem relates the integral over a surface of the curl of a vector field to a line integral around the boundary of that surface: #92;int#95;S#92;nabla#92;times#92;mathbf#123;F#125;#92;cdotd#92;mathbf#123;S#125;#61;#92;int#95;#123;#

An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;

• The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant.

An indefinite integral: the result of the application of such an operation onto a function together with an indefinite domain, yielding a function; a function's antiderivative;; The fluent of a given fluxion in Newtonian calculus.historicalobsolete