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İlk bölümde integral kavramı ve türevle ilişkisi anlatılırken, ikinci bölümde integral hesaplama yöntemleri (kuvvetlerin integrali, köklerin integrali, değişken değiştirme metodu) detaylandırılmaktadır. Son bölümde ise integral ile alan hesaplamaları (x ekseni ile fonksiyon arasındaki alan, y ekseni ile fonksiyon arasındaki alan, iki eğri arasındaki alan) örneklerle açıklanmaktadır.","Videoda her konu için örnekler çözülerek konunun uygulamalı anlatımı yapılmakta ve özellikle parabolik fonksiyonların altındaki alan hesaplamalarında kullanılan \"taban çarpı yükseklik bölü üç\" formülü gibi pratik bilgiler paylaşılmaktadır."]},"endTime":1384,"title":"İntegral Kavramı ve Hesaplama Teknikleri Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral Kavramı ve Temel Özellikleri","list":{"type":"unordered","items":["İntegral, türev ile çok ilişkili bir kavramdır; f fonksiyonunun türevi küçük f fonksiyonuna eşit ise veya fx+c fonksiyonunun türevi küçük f fonksiyonuna eşit ise integral fx dx, büyük fx+c'dir.","İntegral alma işlemi, içerideki ifadenin türevinin alınmamış halini bulmak ve yanına bir C sabiti eklemektir.","İntegral ifadesindeki dx, diferansiyel kavramını temsil eder ve türev alma işleminde dy/dx şeklinde yazılan türev formülünden türetilir."]},"beginTime":3,"endTime":134,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=3&ask_summarization=1"},{"index":1,"title":"Belirsiz İntegral ve Genel Formül","list":{"type":"unordered","items":["Belirsiz integral, integralin altında ve üstünde herhangi bir sınır olmadan hesaplanan integrallerdir.","x üzeri n'in integrali alındığında genel formül x üzeri (n+1) bölü (n+1) + C şeklindedir.","İntegral alma işlemi, fonksiyonun kuvvetini bir arttırıp elde edilen kuvvete bölmekle ve yanına bir sabit ekleyerek yapılır."]},"beginTime":134,"endTime":233,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=134&ask_summarization=1"},{"index":2,"title":"İntegral Alma Kuralları","list":{"type":"unordered","items":["1 dx ifadesinin integrali x + C'dir.","a dx şeklindeki ifadelerin integralleri ax + C şeklinde ifade edilir.","x üzeri eksi beş dx ifadesinin integrali, değişkenin kuvvetini bir arttırıp kuvvete bölerek -x üzeri eksi dört bölü dört + C olarak bulunur."]},"beginTime":233,"endTime":332,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=233&ask_summarization=1"},{"index":3,"title":"İntegral Hesaplama Kuralları","list":{"type":"unordered","items":["Kök x ifadesi integral hesaplamasında x'in kuvveti şeklinde yazılmalı ve kuvvet bir arttırılarak hesaplanır.","Çarpma işlemi yaparken tabanlar aynı ise kuvvetler toplanır, örneğin x² × x^(1/3) = x^(7/3) şeklinde yazılabilir.","Toplam veya fark şeklinde verilen fonksiyonların integrali, ayrı ayrı fonksiyonların integrallerinin toplamı veya farkına eşittir."]},"beginTime":340,"endTime":492,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=340&ask_summarization=1"},{"index":4,"title":"Türev ve İntegral İlişkisi","list":{"type":"unordered","items":["İntegral içerisinde türev ifadesiyle karşılaşılırsa, fonksiyon f(x) + C olarak dışarı çıkar.","İntegralin türevi alınması durumunda, integral dışına çıkan C sabiti tekrar türev alındığı için yok olur ve sadece f(x) olarak çıkar."]},"beginTime":492,"endTime":528,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=492&ask_summarization=1"},{"index":5,"title":"Değişken Değiştirme Metodu","list":{"type":"unordered","items":["İntegrali bildiğimiz yollarla alamadığımız durumlarda değişken değiştirme metodu kullanılır.","Değişken değiştirme metodu, bileşke fonksiyonlarda u = g(x) dönüşümü yaparak ifadeyi daha basit hale getirmeyi amaçlar.","Dönüşümde dx yerine du/dx ifadesi kullanılır ve integral f(u)du şeklinde yazılır."]},"beginTime":528,"endTime":653,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=528&ask_summarization=1"},{"index":6,"title":"Değişken Değiştirme Örnekleri","list":{"type":"unordered","items":["Karmaşık ifadelerde değişken değiştirme yaparak integral hesaplaması kolaylaştırılabilir.","Örneğin, (x² - 5x + 4)⁸ ifadesinde u = x² - 5x + 4 dönüşümü yapılarak integral hesaplanabilir.","Kök içeren ifadelerde de değişken değiştirme yapılabilir, örneğin √(x+1) ifadesinde u = √(x+1) dönüşümü yapılabilir."]},"beginTime":653,"endTime":866,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=653&ask_summarization=1"},{"index":7,"title":"Belirli İntegral","list":{"type":"unordered","items":["Belirli integralin belirsiz integralden tek farkı alt ve üst sınır olarak bir aralık belirtmesidir.","Belirli integralde sabit sayı (C) yazmaya gerek yoktur çünkü üst ve alt sınırlarda hesaplandığında sadeleşir.","Belirli integralin özellikleri: alt ve üst sınır aynıysa integral sıfıra eşittir, sınırlar yer değiştirince integral negatif işaret alır."]},"beginTime":866,"endTime":976,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=866&ask_summarization=1"},{"index":8,"title":"İntegralin Bölünme Özelliği","list":{"type":"unordered","items":["İntegralin bölünme özelliği, parçalı fonksiyonlarda sıkça kullanılır ve a'dan b'ye giderken, aralık içindeki bir c sayısı için ∫ₐᶜ f(x)dx + ∫ᶜᵇ f(x)dx = ∫ₐᵇ f(x)dx eşitliği sağlanır.","Örneğin, ∫₂⁶ f(x)dx ifadesi 3'e göre parçalanarak ∫₂³ f(x)dx + ∫₃⁶ f(x)dx şeklinde yazılabilir.","Verilen örnekte, ∫₁⁴ f(x)dx = 26, ∫₃⁴ f(x)dx = 12 olduğunda, ∫₁³ f(x)dx = 14 olarak bulunur."]},"beginTime":987,"endTime":1098,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=987&ask_summarization=1"},{"index":9,"title":"İntegral ile Alan Hesabı","list":{"type":"unordered","items":["Bir fonksiyonun x ekseni ile arasında kalan alanı bulmak için sınırlar ve fonksiyonun integrali gereklidir.","Y ekseninde pozitif değer alan fonksiyonların alanı ∫ₐᵇ f(x)dx olarak hesaplanırken, negatif değer alan fonksiyonların alanı -∫ₐᵇ f(x)dx şeklinde bulunur.","Hem x ekseninin üzerinde hem de altında görüntüye sahip fonksiyonların alanı, dönüm noktasından ikiye parçalanarak hesaplanır: ∫ₐᶜ f(x)dx - ∫ᶜᵇ f(x)dx."]},"beginTime":1098,"endTime":1207,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=1098&ask_summarization=1"},{"index":10,"title":"Özel Alan Hesaplamaları","list":{"type":"unordered","items":["x² şeklindeki parabolün x ekseniyle arasında kalan alan, taban çarpı yükseklik bölü üç formülüyle hesaplanabilir: S = (a × a²) / 3 = a³/3.","İki eğri veya bir eğri ile bir doğru arasındaki bölge, üstteki fonksiyonun integralinden alttaki fonksiyonun integrali çıkarılarak bulunur.","İki eğri arasındaki alan hesaplamasında, alt ve üst sınırlar bu eğrilerin kesişim noktaları olarak belirlenir."]},"beginTime":1207,"endTime":1381,"href":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=1207&ask_summarization=1"}],"linkTemplate":"/video/preview/15887511750131462880?parent-reqid=1769519829569255-18274168621229239124-balancer-l7leveler-kubr-yp-vla-183-BAL&text=Integral+-+Topic&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"23 minute integral / topic summary / review","related_orig_text":"Integral - Topic","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Integral - 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