Application To Definite Integrals
Passing from the case of indefinite integrals to the case of integrals over an interval, we get exactly the same form of rule (the arbitrary constant of integration disappears).
Read more about this topic: Sum Rule In Integration
Famous quotes containing the words application to, application and/or definite:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (15961650)
“It is known that Whistler when asked how long it took him to paint one of his nocturnes answered: All of my life. With the same rigor he could have said that all of the centuries that preceded the moment when he painted were necessary. From that correct application of the law of causality it follows that the slightest event presupposes the inconceivable universe and, conversely, that the universe needs even the slightest of events.”
—Jorge Luis Borges (18991986)
“Mathematics may be compared to a mill of exquisite workmanship, which grinds your stuff of any degree of fineness; but nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat- flour from peascods, so pages of formulae will not get a definite result out of loose data.”
—Thomas Henry Huxley (182595)