The difference between Integral and Necessary
When used as nouns, 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, whereas necessary means a place to do the "necessary" business of urination and defecation: an outhouse or lavatory.
When used as adjectives, integral means constituting a whole together with other parts or factors, whereas necessary means required, essential, whether logically inescapable or needed in order to achieve a desired result or avoid some penalty.
check bellow for the other definitions of Integral and Necessary
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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."
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Necessary as an adjective:
Required, essential, whether logically inescapable or needed in order to achieve a desired result or avoid some penalty.
Examples:
"Although I wished to think that all was false, it was yet [[necessary]] that that I, who thus thought, must in some sense exist."
"It is absolutely [[necessary]] that you call and confirm your appointment."
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Necessary as an adjective:
Unavoidable, inevitable.
Examples:
"If it is absolutely [[necessary]] to use public computers, you should plan ahead and forward your e-mail to a temporary, disposable account."
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Necessary as an adjective (obsolete):
Determined, involuntary: acting from compulsion rather than free will.
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Necessary as a noun (UK, archaic, _, euphemism, usually with the definite article):
A place to do the "necessary" business of urination and defecation: an outhouse or lavatory.