adj, name, noun ·Common ·High school level
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"The integral of a univariate real-valued function is the area under its curve; but be warned! Not all functions are integrable!"
"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;#123;x#125;dx#61;#92;ln(2), but #92;int#95;0¹#92;frac#123;1#125;#123;x#125;dx#61;#92;infty."
"The integral of x² is #92;frac#123;x³#125;#123;3#125; plus a constant."
"Ceasing to do evil, and doing good, are the two great integral parts that complete this duty."
"A local motion keepeth bodies integral."
"Death is an integral part of life."
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 long s: ∫, or a variant thereof.
Common synonyms include: a certain, actions, aggregate, algorismic, algorithmic, aliquot.
Death is an integral part of life.
Pronounced /ˈɪntəɡɹəl/.
Borrowed from Middle French integral, from Medieval Latin integrālis, from Latin integer (“entire”); see integer.