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https://drive.google.com/file/d/1CPxI... integral -1 (belirsiz integral) • İntegral 1/4 | PDF | Belirsiz İntegral | ... integral-2 belirli integral • İntegral 2/4 | PDF | Belirli İntegral | K...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3413705/2b43d4dc5c37f0b77bae2cc57d034c4d/564x318_1"},"target":"_self","position":"3","reqid":"1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=videoid:12742216769714818952","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik öğretmeni Mustafa Güler tarafından sunulan bir eğitim içeriğidir. Öğretmen, tahtada notlar alarak ve öğrencilere sorular sorarak konuyu açıklamaktadır.","Video, integral konusunun temel kavramlarını, türev ile integral arasındaki ilişkiyi ve alan hesaplama tekniklerini kapsamaktadır. İçerik üç ana bölümden oluşmaktadır: ilk bölümde integral kavramı ve belirli integral ile normal integral arasındaki farklar anlatılırken, ikinci bölümde değişken değiştirme yöntemi ve alan hesaplama teknikleri ele alınmaktadır. Son bölümde ise farklı fonksiyonların oluşturduğu alanların hesaplanması ve \"ayrancı arası\" kavramı açıklanmaktadır.","Videoda belirli integrallerin alan hesaplamaları için kullanımı, belirli integrallerin sonuçlarının reel sayı olması, sıfır olan durumlar (a'dan a'ya, tek fonksiyonlar, çift fonksiyonlar), iki eğri arasındaki alan hesaplaması için üstten alttan çıkarma yöntemi ve y eksenine göre alan hesaplaması için ters fonksiyon kullanımı gibi konular detaylı olarak örneklerle pekiştirilmektedir."]},"endTime":1432,"title":"Matematik Dersi: İntegral ve Alan Hesaplama","beginTime":0}],"fullResult":[{"index":0,"title":"Türev Kavramı","list":{"type":"unordered","items":["Matematik öğretmeni Mustafa Güler, türev kavramını açıklıyor.","\"d/dx\" ifadesi x'e göre türev almayı, \"d/dy\" ifadesi y'ye göre türev almayı gösterir.","Sabit sayının türevi sıfırdır."]},"beginTime":42,"endTime":128,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=42&ask_summarization=1"},{"index":1,"title":"İntegral Kavramı","list":{"type":"unordered","items":["İntegral, türev işleminin tam tersidir; üstteki sayı bir arttırılır ve aynısı paydaya yazılır.","İntegral sorularında her zaman \"C\" sabiti bulunur.","İntegral, türev işleminin tersi olduğundan, türev ile başlayan sorularda \"C\" bulunmaz."]},"beginTime":128,"endTime":245,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=128&ask_summarization=1"},{"index":2,"title":"Belirli İntegral","list":{"type":"unordered","items":["Belirli integral, üst ve alt sınırlar arasında integral alınarak hesaplanır.","Belirli integral, bir alan sorusunu temsil eder.","Belirli integralde, üst sınırdan alt sınır çıkarıldığında sonuç elde edilir."]},"beginTime":245,"endTime":419,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=245&ask_summarization=1"},{"index":3,"title":"Belirli İntegralin Özellikleri","list":{"type":"unordered","items":["Belirli integral sonucu her zaman reel sayıdır.","Tek fonksiyonların a'dan a'ya integrali sıfırdır.","Çift fonksiyonların a'dan a'ya integrali, sıfırdan a'ya integralin iki katıdır.","İntegral sınırları yer değiştirildiğinde, integralin önüne eksi işareti gelir.","İntegral sınırları parçalanabilir, özellikle mutlak değer ve parçalı fonksiyonlarda kullanılır."]},"beginTime":419,"endTime":561,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=419&ask_summarization=1"},{"index":4,"title":"Türev ve İntegral İlişkisi","list":{"type":"unordered","items":["Türev, integral ile birlikte kullanıldığında, türevin hepsinin üstüne çekilmesi mümkündür.","Türev integrali götürdüğünde, geriye f(x) + C şeklinde bir sonuç kalır.","Türevi herkese ait yapmak için, türevin içindekinin türevini paydaya yazmak gerekir."]},"beginTime":566,"endTime":644,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=566&ask_summarization=1"},{"index":5,"title":"İntegral Hesaplama Örnekleri","list":{"type":"unordered","items":["Türev integrali götürdüğünde, f(5x) / 5 şeklinde bir sonuç elde edilir.","İntegral hesaplanırken, sınırlar belirlenir ve integral alınır.","İntegral hesaplandıktan sonra, f(2) = 6 şeklinde bir sonuç bulunur."]},"beginTime":644,"endTime":872,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=644&ask_summarization=1"},{"index":6,"title":"Değişken Değiştirme Yöntemi","list":{"type":"unordered","items":["Değişken değiştirme yönteminde, çarpmalı ve bölmeli işlemlerde değişken değiştirme yapılır.","Değişken değiştirme yaparken, bir yere \"u\" denildiğinde, dışarıdan türev olmalıdır.","Değişken değiştirme yapıldıktan sonra, yeni integral hesaplanır ve sınırlar yerine konulur."]},"beginTime":872,"endTime":1034,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=872&ask_summarization=1"},{"index":7,"title":"Alan Hesaplama","list":{"type":"unordered","items":["x ekseni ile f(x) grafiği arasındaki alan, a'dan b'ye f(x) dx şeklinde hesaplanır.","x ekseninin altındaysa, alan -∫a'dan b'ye f(x) dx şeklinde hesaplanır.","İki eğri arasındaki alan, üsttekinden alttakini çıkararak hesaplanır."]},"beginTime":1034,"endTime":1241,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=1034&ask_summarization=1"},{"index":8,"title":"Y Eksenine Göre Alan Hesaplama","list":{"type":"unordered","items":["Y eksenine göre alan hesaplanırken, f(x) yerine f(x)'in tersi alınır.","Y ekseninin sağında ise alan artı, solunda ise eksi olarak hesaplanır.","İki eğri arasındaki alan, y eksenine göre hesaplanırken her zaman sağdakinden soldaki çıkarılır."]},"beginTime":1241,"endTime":1317,"href":"/video/preview/12742216769714818952?parent-reqid=1769846396890341-1761315471422984454-balancer-l7leveler-kubr-yp-sas-41-BAL&text=Integral+Web+Solution&t=1241&ask_summarization=1"},{"index":9,"title":"Fonksiyonların Alanları","list":{"type":"unordered","items":["Ayrancı arası ifadesi, f(x) 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