Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if f is a continuous real-valued function defined on a closed interval, then, once an antiderivative F of f is known, the definite integral of f over that interval is given by

Through history, Metz population has been impacted by the vicissitudes of the wars and the annexations involving the city and avoiding a continuous population growth.

Through maneuver and continuous assault, Chinese, Persian, Arab and Eastern European armies could be stressed until they broke, and then were annihilated in pursuit.

Through daily efforts to rebuild, re-arm and improve the fortifications, he was able to finally connect them with a continuous defence system enceinte.

Through touring heavily throughout 1999 and 2000, Guided by Voices ' live act became legendary, with shows often stretching past the three-hour mark, and populated by an endless stream of new and classic songs, Pollard solo tracks, impromptu covers of The Who, David Bowie and The Rolling Stones, all accompanied by continuous alcohol consumption.

Through September 28, for example, Alabama ’ s 117th Air Refueling Wing kept aircraft aloft on a continuous basis.

Through innuendo, rumors, and public discrediting, a hostile environment is created in which one individual gathers others to willingly, or unwillingly, participate in continuous malevolent actions to force a person out of the workplace.

Through this strategy, 40 million bank and investment accounts were quietly converted into war bonds, providing the Reich government with a continuous supply of money.

Through the continuous cycle of learning, teacher ’ s often work with students to develop a framework of knowledge, which is to be evaluated based on student input to the lessons content.

Through unusual animation techniques the illusion is created that the film consists of one continuous shot or long take.

Through continuous research, their work is to identify and translate documents and texts that shed new insight into this important period of history.

Through this monitoring system, the concept of continuous self-upgrading and development after a training course can be impacted on all teachers in Rizal Province.

Through this area, it had a continuous center turn lane, losing the grassy median it had in places downtown.

His second book was The Man Who Walked Through Time ( 1968 ), in which Fletcher was the first person to walk a continuous route through Grand Canyon National Park in 1963.

Through the establishment of the SERC, the University seeks to help and support the local software industry in establishing and improving their processes and practices through continuous feedback and training.

Through the House of Burgesses, the Virginia House of Delegates is considered the oldest continuous legislative body in the New World.

Through continuous innovations, Rodenstock further expanded its market share during that time.

" Through continuous struggle the Afghan Mujahideen succeeded in their mission, and the Russian forces withdrew from Afghanistan in 1989 after the loss of tens of thousands of its soldiers.

Through user contribution, Razor establishes a distributed and constantly updating catalogue of spam in propagation that is consulted by email clients to filter out known spam.

Through its membership and the National Plant Collection Holders, the NCCPG seeks to rediscover and reintroduce endangered garden plants by encouraging their propagation and distribution so that they are grown as widely as possible.

Through consideration of it, Cantor and others helped lay the foundations of modern general topology.

Through such people as Nikola Tesla, Galileo Ferraris, Oliver Heaviside, Thomas Edison, Ottó Bláthy, Ányos Jedlik, Sir Charles Parsons, Joseph Swan, George Westinghouse, Ernst Werner von Siemens, Alexander Graham Bell and Lord Kelvin, electricity was turned from a scientific curiosity into an essential tool for modern life, becoming a driving force for the Second Industrial Revolution.

Through centuries of international convention, this has become the dominant rule to identifying an emperor in the modern era.

The grail is central in many modern Arthurian works, including Charles Williams's novel War in Heaven and his two collections of poems about Taliessin, Taliessin Through Logres and Region of the Summer Stars, and in feminist author Rosalind Miles ' Child of the Holy Grail.

However, the foundation of memetics in full modern incarnation originates in the publication in 1996 of two books by authors outside the academic mainstream: Virus of the Mind: The New Science of the Meme by former Microsoft executive turned motivational speaker and professional poker player, Richard Brodie, and Thought Contagion: How Belief Spreads Through Society by Aaron Lynch, a mathematician and philosopher who worked for many years as an engineer at Fermilab.

Through collaboration with the International Rice Research Institute ( IRRI ), 52 modern rice varieties were released in the country between 1966 and 1997, helping increase national rice production to 14 million tons in 1987 and to 19 million tons in 1996.

) Through much of the modern era, it was thought that play texts were popular items among Renaissance readers that provided healthy profits for the stationers who printed and sold them.

Through the infusion of EU investment funds, the city continues to work to reshape itself into a modern metropolis.

Through their own experiments and interest in arthropods and death, Song Ci, Francesco Redi, Bergeret d ’ Arbois, Jean Pierre Mégnin and the German doctor Hermann Reinhard have helped to lay the foundations for today's modern forensic entomology.

It is elaborated upon in modern English poetry, such as Tennyson's Idylls of the King and Charles Williams's Taliessin Through Logres.

Through a process of language assimilation, the sequence has resulted in the modern pronunciation of.

Through the same linguistic route, cods became a modern slang term for the male genitalia.

Some people, such as the following authors, have inferred, insinuated, or suggested that entering a state of perpetual war becomes progressively easier in a modern democratic republic, such as the United States, due to the development of a relationship network between people who wield political and economic power also owning capital in companies that financially profit from war, lobby for war, and influence public opinion of war through influence of Mass media outlets that control the presentation for the causes of war, the effects of war, and the Censorship of war: ( 1 ) " The Iron Triangle: Inside the Secret World of the Carlyle Group " ( 2004 )" by Dan Briody ; ( 2 ) " The Pentagon Labyrinth: 10 Short Essays to Help You Through It " ( 2011 ) an anthology by nine authors who are Pierre M. Sprey, George Wilson, Franklin C. Spinney, Bruce I. Gudmundsson, Col. G. I. Wilson, Col. Chet Richards, Andrew Cockburn, Thomas Christie, and Winslow T. Wheeler ; ( 3 ) " Prophets of War: Lockheed Martin and the Making of the Military-Industrial Complex " ( 2010 ), by William D. Hartung ; ( 4 ) " Media Control, Second Edition: The Spectacular Achievements of Propaganda ( 2002 ), by Noam Chomsky ; and ( 5 ) " Manufacturing Consent: The Political Economy of the Mass Media " ( 2002 ), by Edward S. Herman and Noam Chomsky.

In 2010, a documentary entitled " A Journey Through the Weald of Kent " was produced by Buff Films, JR Films and Cranbrook school to document the Weald's place in modern England.

** Through her son, Françoise Marie became a direct ancestor of Louis-Philippe I, King of the French and the modern House of Orléans.

Through three of her children ( Louise Françoise de Bourbon, Françoise Marie de Bourbon and the comte de Toulouse ), Madame de Montespan became an ancestor of the modern House of Orléans and its present head, Henri d ' Orléans, Count of Paris and Duke of France.

Through his last victory over Mehmed II at the siege of Belgrade ( in modern Serbia ) in 1456, he saved the kingdom from Ottoman occupation for several decades.

" Through the years of 1927 and 1962, thirteen patents were granted to inventors for snow vehicles considered the predecessors to the modern snowmobile.

J. Vernon McGee of the Through the Bible radio program may be the best exemplar of the purely expository method of preaching in modern American times.

Through her writings, she instructed and inspired women to take on the modern gender roles which were so common in Europe and North America.

The film was also perceived by many, including its screenwriter and co-producer Bruce Joel Rubin, as a modern interpretation of the Liberation Through Hearing During The Intermediate State, Tibetan Book of the Dead.

Jane was also known as O-bah-bahm-wawa-ge-zhe-go-qua ( or Obabaamwewe-giizhigokwe in modern spelling ) ( The Woman of the Sound the Stars Make Rushing Through the Sky ).

Through Benoni, Nathaniel has a large number of modern descendants.

Through the process of transition from a traditional Confucian notion of civilization to a Western notion of acceptance and resistance, Koreans shaped their civilization as well as their notions of the racial, cultural, and individual modern self.