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== Sejarah ==
{{lihat juga|Sejarah kalkulus}}
=== Kamiran sebelum penerbitan kalkulus ===
=== Pre-calculus integration ===
IntegrationKamiran cantelah bediguna tracedpakai assejak farzaman backMesir aspurba ancient Egyptlagi ''ca.'' 1800 BC, withdimana thePapirus Matematik [[Moscow (Moscow Mathematical Papyrus]]) demonstratingtelah knowledgemenunjukkan offormula auntuk formulamenyelesaikan formasalah theberkaitan [[volume]]piramid. of aTeknik pyramidalpertama [[frustum]].yang Thesistematik firstdan documentedtersusun systematicdalam techniquemenyelesaikan capablemasalah ofkamiran determiningadalah integralskaedah ispenyusutan the(exhaustion [[method) of exhaustion]] ofoleh [[Eudoxus of Cnidus|Eudoxus]] (''ca.'' 370 BC),. whichKaedah soughtini todigunakan finduntuk areasmencari andluas volumeskawasan bydengan breakingmemecahkan themkawasan upitu intokepada ankawasan-kawasan infinitekecil numberyang ofluasnya shapesdiketahui. forKaedah whichini thejuga areaboleh ordigunakan volumeuntuk wasmencari knownisipadu. ThisArchimedes methodmenggunakan waskaedah furtherpenyusutan developeduntuk andmengira employednilai byπ, luas [[Archimedesbulatan]] anddan used to calculate areas forluas [[parabola]]s and an approximation to the area of a circle. SimilarKaedah methodsyang werehampir independentlysama developedtelah indibina Chinaoleh aroundahli thematematik 3rdCina century AD by [[Liu Hui]], whojuga useduntuk itmencari toluas find the area of the circlebulatan. ThisKaedah methodLiu wasHui laterpula useddikembangkan inoleh thepasangan 5thayah centurydan byanak Chinese father-and-son mathematicians [[Zu Chongzhi]] anddan [[Zu Geng (mathematician)|Zuuntuk Geng]] to find the volume ofmencari aisipadu spheresfera.<ref>{{citation | last1=Shea | first1=Marilyn | title=Biography of Zu Chongzhi | date=May 2007 | url=http://hua.umf.maine.edu/China/astronomy/tianpage/0014ZuChongzhi9296bw.html | publisher=University of Maine | accessdate=9 January 2009}}<br>{{Citation | last1=Katz | first1=Victor J. | title=A History of Mathematics, Brief Version | publisher=[[Addison-Wesley]] | isbn=978-0-321-16193-2 | year=2004 | pages=125–126}}</ref> ThatAbad sameyang centurysama, theahli [[Indianmatematik mathematics|IndianIndia mathematician]] [[Aryabhata]] usedmenggunakan akaedah similaryang methodhampir insama orderuntuk to find the volume ofmencari aluas [[cubekiub]].<ref>Victor J. Katz (1995), "Ideas of Calculus in Islam and India", ''Mathematics Magazine'' '''68''' (3): 163-174 [165]</ref>
TheLangkah nextseterusnya majordalam stepperkembangan inkamiran integraladalah calculusdi cameIraq inapabila [[Abbasidahli Caliphate|Iraq]]matematik whenIslam theabad [[Islamic_mathematics|11th century mathematician]]ke-11, [[Ibn alAl-Haytham]]Haitham (known asatau ''Alhazen'' indi EuropeEropah) devisedmerancang whatsatu ismasalah nowyang knownkini asdikenali sebagai "Alhazen'smasalah problemAl-Haitham", whichdalam leadsbuku tofiziknya an"Kitab [[Quartic equation|equation of the fourth degree]], in hisAl-Manazir" (''[[Book of Optics]]''. Whileatau solvingBuku thistentang problem,Penglihatan). heMasalah performedini anmembawa integrationkepada inpersamaan orderdarjah tokeempat find(iaitu thepersamaan volumeyang ofmelibatkan akuasa [[paraboloid]].4 Usingatau [[mathematical''x''<sup>4</sup>). induction]],Semasa hemenyelesaikan waspermasalahan ableini, tobeliau generalizetelah hismenggunakan resultkamiran foruntuk themencari integralsisipadu ofparaboloid. [[polynomial]]sMenggunakan upinduksi tomatematik themelalui [[Quarticpengiraan, polynomial|fourthbeliau degree]].telah Hemengasaskan thuskamiran cameuntuk closepolinomial todarjah findingkeempat. aNamun generalIbn formula for the integrals of polynomials, butAl-Haitham hetidak was notmengambil concernedberat withakan anypolinomial polynomialsdengan higherdarjah thanlebih thetinggi fourthdari degree4.<ref name=Katz>Victor J. Katz (1995), "Ideas of Calculus in Islam and India", ''Mathematics Magazine'' '''68''' (3): 163–174 [165–9 & 173–4]</ref> SomeSelain ideasIbn ofAl-Haitham, integralide-ide calculustentang arekamiran alsojuga foundboleh inditemui thedalam buku astronomi ''Siddhanta Shiromani'', ayang 12thditulis centuryoleh [[Indianahli astronomy|astronomy]]matematik textIndia byBhaskara IndianII mathematicianpada [[Bhāskarakurun II]]ke-12.
Kemajuan seterusnya muncul pada kurun ke-16. Pada masa ini asas kalkulus moden telah tercipta melalui pengiraan yang dibuat oleh Cavalieri dengan [[prinsip Cavalieri]] dan kerja-kerja Fermat. Langkah untuk penciptaan kalkulus moden ini semakin dikukuhkan oleh Barrow dan [[Torricelli]] pada awal kurun ke-17 apabila kedua-duanya menyatakan terdapat hubungan antara pembezaan dan kamiran.
The next significant advances in integral calculus did not begin to appear until the 16th century. At this time the work of [[Bonaventura Cavalieri|Cavalieri]] with his [[Cavalieri's principle|''method of indivisibles'']], and work by [[Pierre de Fermat|Fermat]], began to lay the foundations of modern calculus. Further steps were made in the early 17th century by [[Isaac Barrow|Barrow]] and [[Evangelista Torricelli|Torricelli]], who provided the first hints of a connection between integration and [[Differential calculus|differentiation]].
AtPada aroundmasa theyang samehampir timesama, thereahli wasmatematik alsoJepun ajuga greatbanyak dealmembuat ofpengiraan work being done by [[Japanese mathematics|Japanese mathematicians]]kamiran, particularly byterutama [[Seki Kōwa]].<ref>http://www2.gol.com/users/coynerhm/0598rothman.html</ref> Beliau Hemembuat madebeberapa asumbangan numberseperti ofmengaplikasikan contributions,kaedah namelypenyusutan inuntuk methodsmencari ofluas determiningkawasan areasmelalui of figures using integrals, extending the [[method of exhaustion]]kamiran.
=== Newton and Leibniz ===
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