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Öğretmen, tahtada türev ve integral konularını adım adım anlatmaktadır.","Video, integralin yedi videosunun devamı niteliğindedir ve özellikle C sabiti hesaplama konusunu ele almaktadır. İçerikte toplam 12 soru çözülmekte olup, sorular en kolaydan en zora doğru sıralanmıştır. Öğretmen, türev ve integral arasındaki ilişkiyi kullanarak çeşitli örnekler üzerinden C sabitini bulma yöntemlerini göstermektedir.","Videoda 77. ve 78. sorular detaylı olarak çözülmekte, EV türev fonksiyonu kullanılarak fonksiyonlar bulunmakta ve belirli değerlerde fonksiyonların değerleri hesaplanmaktadır. Ayrıca, sonraki videolarda grafikli sorular ve değişken değiştirme konuları ele alınacağı belirtilmekte ve sınavlarda türev ve integral konusundan 3-4 soru çıkabileceği bilgisi paylaşılmaktadır."]},"endTime":1529,"title":"İntegral ve Türev Dersi: C Sabiti Hesaplama ve Soru Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral ve Sabit Terim","list":{"type":"unordered","items":["İntegralin yedinci videosunda C sabit terim hesaplaması yapılacak.","İntegral alarak türev fonksiyonundan orijinal fonksiyona geçiş yapılabilir.","İntegral alırken sabit terim (C) unutulmamalıdır."]},"beginTime":8,"endTime":32,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=8&ask_summarization=1"},{"index":1,"title":"İntegral Örneği","list":{"type":"unordered","items":["f'(x) = 4x - 3 verilmiş ve f(2) = 5 bilgisi kullanılarak C sabit terimi bulunur.","İntegral alınarak f(x) = 2x² - 3x + C elde edilir ve f(2) = 5 bilgisiyle C = 3 bulunur.","f(0) = 3 olarak hesaplanır."]},"beginTime":32,"endTime":124,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=32&ask_summarization=1"},{"index":2,"title":"İkinci Türev ve İntegral","list":{"type":"unordered","items":["f''(x) = 2x + 4 verilmiş, f'(1) = 2 ve f(1) = 0 ile ilgili bilgiler kullanılarak C sabit terimleri bulunur.","İntegral alınarak f'(x) = x² + 2x + C₁ elde edilir ve f'(1) = 2 bilgisiyle C₁ = -3 bulunur.","İkinci integral alınarak f(x) = x³/3 + 2x² - 3x + C₂ elde edilir ve f(1) = 0 ile ilgili bilgilerle C₂ = 1/3 bulunur."]},"beginTime":124,"endTime":306,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=124&ask_summarization=1"},{"index":3,"title":"Diferansiyel ve İntegral","list":{"type":"unordered","items":["f'(x) = 5 (x-3) diferansiyeli verilmiş ve f(-2) sorulmuş.","İntegral alınarak f(x) = 5x - 4 + C elde edilir ve f(3) = 11 bilgisiyle C = -4 bulunur.","f(-2) = -14 olarak hesaplanır."]},"beginTime":306,"endTime":398,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=306&ask_summarization=1"},{"index":4,"title":"İntegral ve Sabit Terim Örneği","list":{"type":"unordered","items":["f''(x) = 6x² - 2x ve f(6) = 0 ile ilgili bilgiler kullanılarak C sabit terimi bulunur.","İntegral alınarak f'(x) = 3x² - 2x + C elde edilir ve f(6) = 0 ile ilgili bilgilerle C = 12 bulunur.","f(2) = 10 olarak hesaplanır."]},"beginTime":398,"endTime":579,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=398&ask_summarization=1"},{"index":5,"title":"İntegral ve Sabit Terim Uygulaması","list":{"type":"unordered","items":["f'(x) = 4x ve f(2) = 13 ile ilgili bilgiler kullanılarak C sabit terimi bulunur.","İntegral alınarak f(x) = 2x³ - 2x² + C elde edilir ve f(2) = 13 bilgisiyle C = -5 bulunur.","f(-1) = 7 olarak hesaplanır."]},"beginTime":579,"endTime":733,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=579&ask_summarization=1"},{"index":6,"title":"İntegral ve Türev Problemi Çözümü","list":{"type":"unordered","items":["Verilen problemde f'(x) = 6x² ve f'(1) = 15 bilgileri kullanılarak f(x) fonksiyonu bulunuyor.","Önce f'(x) fonksiyonunun integrali alınarak f(x) = 3x³ + 2x + C₁ elde ediliyor.","f(1) = 4 bilgisi kullanılarak C₁ = 1 bulunuyor ve f(x) = x³ + 2x + 1 olarak tamamlanıyor.","f(-1) değeri hesaplanarak cevap -2 olarak bulunuyor."]},"beginTime":738,"endTime":920,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=738&ask_summarization=1"},{"index":7,"title":"Karmaşık İntegral Problemi","list":{"type":"unordered","items":["f(x) = ∫(g(x) + x·g'(x)) dx şeklinde verilen karmaşık bir integral problemi çözülüyor.","İntegral ifadesi, x·g(x) çarpımının türevi şeklinde yeniden yazılıyor.","f(3) = 6 bilgisi kullanılarak C = -12 bulunuyor ve f(0) değeri hesaplanarak cevap -1 olarak bulunuyor."]},"beginTime":920,"endTime":1053,"href":"/video/preview/13074644726301872552?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=920&ask_summarization=1"},{"index":8,"title":"Türev ve İntegral Soruları","list":{"type":"unordered","items":["Toplam on iki soru çözülecek, türev ve integral arasındaki en kolaydan en zora doğru farklı işlemlerin olduğu sorular.","İlk 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Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/222140/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/_chU_wAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"13","reqid":"1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=videoid:9426788986556539746","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitim içeriğidir. Eğitmen, çift katlı integral konusunda örnek bir soru çözümü sunmaktadır.","Videoda, birinci bölgede y = x doğrusu, x ekseni ve y = √(1-x²) eğrisi ile sınırlı bir bölgede cos(x² + y²) integralinin nasıl hesaplanacağı adım adım anlatılmaktadır. Eğitmen önce integral alma bölgesini çizerek sınırları belirleyip, ardından dairesel alan olduğu için kutupsal koordinatları kullanarak integral sınırlarını ve integral alma sırasını açıklamaktadır. Son olarak, integral hesaplaması yapılarak sonucun π/8 sin(1) olduğu gösterilmektedir."]},"endTime":591,"title":"Çift Katlı İntegral Örnek Soru Çözümü","beginTime":0}],"fullResult":[{"index":0,"title":"Çift Katlı İntegral Sorusu","list":{"type":"unordered","items":["Video, çift katlı integral konusunda bir örnek soruyu inceleyecektir.","Soruda, birinci bölgede y=x doğrusu, x ekseni ve y=√(1-x²) eğrisi ile sınırlı bir bölgede cos(x²+y²) integralinin sonucu bulunması istenmektedir.","Çift katlı integral sorularında ilk adım, integral alma bölgesini çizmek ve bu bölge sayesinde integralin sınırlarını ve sırasını belirlemektir."]},"beginTime":1,"endTime":43,"href":"/video/preview/9426788986556539746?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=1&ask_summarization=1"},{"index":1,"title":"İntegral Alma Bölgesinin Çizimi","list":{"type":"unordered","items":["Birinci bölgede, x-y düzleminin birinci bölgesi kastedilmektedir.","İntegral alma bölgesi, y=x doğrusu, x ekseni ve y=√(1-x²) eğrisi ile sınırlıdır.","Çember y=√(1-x²) denklemi, yarıçapı 1 olan bir yarım çemberdir ve x ekseninin üstünde kalır."]},"beginTime":43,"endTime":203,"href":"/video/preview/9426788986556539746?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=43&ask_summarization=1"},{"index":2,"title":"Kutupsal Koordinatların Kullanımı","list":{"type":"unordered","items":["İntegral alma bölgesi dairesel olduğu için kutupsal koordinatlar kullanılmalıdır.","Kutupsal koordinatlarda r yarıçap, 0 ile 1 arasında değişir.","θ açısı, x ekseni ile pozitif yönde yaptığı açıdır ve 0 ile π/4 arasında değişir."]},"beginTime":203,"endTime":341,"href":"/video/preview/9426788986556539746?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=203&ask_summarization=1"},{"index":3,"title":"İntegralin 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Eğitmen, bu işlemi yapmak için üç aşamalı bir yöntem sunmaktadır: sınırlardan x ve y değişim aralıklarını çıkarma, fonksiyon sınırlarını belirleyip çizme ve integral alma sırasını değiştirip hesaplamayı tamamlama. İçerikte çeşitli örnekler üzerinden konu pekiştirilmekte ve sınavlarda integral alma sırasını değiştirmenin ne zaman gerektiğini de açıklanmaktadır.","Ayrıca değişken değiştirme yöntemiyle integral hesaplama da videoda gösterilen konular arasındadır. Her bir örnek için adım adım çözüm sunulmakta ve konunun uygulamalı anlatımı yapılmaktadır."]},"endTime":1481,"title":"Çift Katlı İntegralde İntegral Alma Sırasının Değiştirilmesi","beginTime":0}],"fullResult":[{"index":0,"title":"Çift Katlı İntegralde İntegral Alma Sırasının Değiştirilmesi","list":{"type":"unordered","items":["Çift katlı integralde integral alma sırasının değiştirilmesi örnekler üzerinden işlenecek.","İntegral alma sırasını değiştirmenin nedeni, içteki integralin alınamaması durumunda dıştaki integrali önce hesaplamak için.","Sınıflarda integral hesaplaması istendiğinde sınırlar verilmiş ancak içerideki integral alınamıyorsa, integral sırasını değiştirmek gerekir."]},"beginTime":0,"endTime":94,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=0&ask_summarization=1"},{"index":1,"title":"İntegral Alma Sırasını Değiştirme Adımları","list":{"type":"unordered","items":["İntegral alma sırasını değiştirmek için önce integralden sınırları çıkarmak gerekir.","Fonksiyon sınırları ve sayı sınırlarını belirlemek önemlidir; fonksiyon sınırları varsa doğrudan yer değiştirilemez.","İntegral alma sırasını değiştirmek için önce sınırları çıkartıp, sonra fonksiyon sınırlarından elde edilen fonksiyonları çizeriz."]},"beginTime":94,"endTime":217,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=94&ask_summarization=1"},{"index":2,"title":"Örnek 1 Çözümü","list":{"type":"unordered","items":["Fonksiyon sınırları (y=x ve y=π) ve sayı sınırları (x=0 ile x=π) çizilerek alan belirlenir.","İntegral alma sırası değiştirildiğinde, sayı sınırları y'ye, fonksiyon sınırları ise x'e getirilir.","Değiştirilmiş integral hesaplanarak sonucu 2 olarak buluruz."]},"beginTime":217,"endTime":557,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=217&ask_summarization=1"},{"index":3,"title":"Örnek 2 Çözümü","list":{"type":"unordered","items":["İkinci örnekte fonksiyon sınırları y=x² ve y=9, sayı sınırları ise x=0 ile x=3 olarak belirlenir.","Alan, y=x² eğrisinin alt kısmından y=9 doğrusuna kadar olan bölgedir.","İntegral alma sırası değiştirildiğinde, sayı sınırları 0'dan 9'a, fonksiyon sınırları ise 0'dan y'ye değişir."]},"beginTime":557,"endTime":820,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=557&ask_summarization=1"},{"index":4,"title":"Çift Katlı İntegral Hesaplama","list":{"type":"unordered","items":["İntegral hesaplamasında önce x'e göre integral alınarak sabit kaiden yararlanılır ve x küpün integrali alınır.","İntegral hesaplaması sırasında değişken değiştirme yöntemi kullanılır: y küp = u dönüşümü yapılarak integral daha kolay hesaplanır.","İntegral hesaplaması sonucunda 1/12(e^729 - 1) değeri bulunur."]},"beginTime":845,"endTime":1007,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=845&ask_summarization=1"},{"index":5,"title":"İntegral Alma Sırasını Değiştirme","list":{"type":"unordered","items":["İntegral alma sırasını değiştirmek için öncelikle sınırlar çıkarılır ve fonksiyon sınırları çizilir.","Fonksiyon sınırları x³ = y ve x = 2 olarak belirlenir, grafik çizimi yapılır.","İntegral alma sırası değiştirildiğinde, sayı sınırı x'e (0'dan 2'ye) ve fonksiyon sınırı y'ye (0'dan x³'e) geçer."]},"beginTime":1007,"endTime":1253,"href":"/video/preview/10124146880579618243?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=1007&ask_summarization=1"},{"index":6,"title":"İntegral Alma Sırasını Değiştirme Süreci","list":{"type":"unordered","items":["İntegral alma sırası değiştirildiğinde önce y'ye göre, sonra x'e göre integral alınır.","Değişken değiştirme yöntemi kullanılarak u = x⁴ + 1 dönüşümü yapılır ve integral hesaplanır.","Çift katlı integrallerde integral alma sırasını değiştirmenin üç aşaması vardır: sınırların çıkarılması, fonksiyon sınırlarının belirlenmesi ve integral alma sırasının 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Öğretmen, öğrencilere ders kitabı doldurma ve soru bankasındaki soruları çözmelerini tavsiye etmektedir."]},"endTime":3241,"title":"AYT Matematik: Belirli İntegral Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"AYT Matematik İntegral Dersine Giriş","list":{"type":"unordered","items":["65. gün AYT matematik dersinde integral konusuna başlanıyor.","Son 10 güne girildiği ve 55. videoya ulaşıldığı belirtiliyor.","İntegral konusunda belirsiz integralden sonra belirli integrale geçiliyor."]},"beginTime":0,"endTime":96,"href":"/video/preview/1069462009063213980?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=0&ask_summarization=1"},{"index":1,"title":"Belirli İntegralin Tanımı ve Özellikleri","list":{"type":"unordered","items":["Belirli integral, alt sınır ve üst sınır adı verilen iki sınır arasında hesaplanır.","Belirli integralde, integral işaretinin altına ve üstüne alt sınır ve üst sınır yazılır.","Belirli integralde, 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yerini değiştirdiğimizde integral işaret değiştirir, çift fonksiyonlarda ise işaret değişmez.","Ne tek ne çift olan fonksiyonlarda, -7 ile 7 aralığında integral hesaplandığında sonuç sıfırdan farklı olur."]},"beginTime":1523,"endTime":1604,"href":"/video/preview/1069462009063213980?parent-reqid=1769418207683218-16780852784034367736-balancer-l7leveler-kubr-yp-vla-154-BAL&text=CintegralTV&t=1523&ask_summarization=1"},{"index":13,"title":"İntegral Örnekleri ve Çözüm Yöntemleri","list":{"type":"unordered","items":["Tek fonksiyonlarda, -30 ile 30 aralığında f(x) integrali hesaplanırken, 30 aralığında f(x) integrali sıfır olarak alınır.","Çift fonksiyonlarda, -30 ile 30 aralığında f(x) integrali hesaplanırken, 30 aralığında f(x) integrali de aynı değer olarak alınır.","İntegral hesaplamalarında, fonksiyonların tek veya çift olduğu bilgisi kullanılarak sonuçlar 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