The difference between Antiderivative and Integral
When used as nouns, antiderivative means a function whose derivative is a given function, whereas integral means a number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.
Integral is also adjective with the meaning: constituting a whole together with other parts or factors.
check bellow for the other definitions of Antiderivative and Integral
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Antiderivative as a noun (calculus):
A function whose derivative is a given function; an indefinite integral
Examples:
"synonyms: primitive integral"
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Integral as an adjective:
Constituting a whole together with other parts or factors; not omittable or removable
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Integral as an adjective (mathematics):
Of, pertaining to, or being an integer.
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Integral as an adjective (mathematics):
Relating to integration.
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Integral as an adjective (obsolete):
Whole; undamaged.
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Integral as a noun (mathematics):
A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed.
Examples:
"The integral of <math>x\mapsto x^2</math> on <math>[0,1]</math> is <math>\frac{1}{3}</math>."
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Integral as a noun (mathematics):
Antiderivative
Examples:
"The integral of <math>x^2</math> is <math>\frac{x^3}{3}</math> plus a constant."