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Eğitmen, limit, türev ve integral konularını kapsayan bir dizi eğitim içeriğinin son bölümünü oluşturmaktadır.","Video, integral konusunun AYT sınavındaki önemi vurgulanarak başlayıp, teorik bilgilerin (diferansiyel, belirsiz integral, belirli integral, integral alma kuralları) anlatımıyla devam etmektedir. Daha sonra belirli integral özellikleri, alan hesaplama, Riemann toplamları ve fonksiyonlarla ilgili çeşitli soru çözümleri sunulmaktadır. Video, yaklaşık 30 sorunun sınav hazırlığı ve konu tekrarı için tasarlandığını belirtmektedir.","Eğitmen, konuları adım adım ve örneklerle açıklamakta, türev-integral ilişkisini vurgulayarak ÖSYM sınavlarında çıkabilecek soru tiplerini göstermektedir. Video içeriğinde değişken değiştirme yöntemi, parçalı fonksiyonların integrali, çember yardımıyla alan hesaplama ve Riemann toplamları gibi konular detaylı olarak ele alınmaktadır."]},"endTime":10982,"title":"AYT Matematik Full Tekrar Serisi: İntegral","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral Konusuna Giriş","list":{"type":"unordered","items":["AYT full tekrar serisinin son konusu olan integral, her sene mutlaka dört tane soru olarak sınavda karşımıza çıkar.","İntegral, AYT matematikte hedeflerin yüksek olan öğrencilerin mutlaka bilmeleri gereken konulardan biridir.","Geçen sene ÖSYM'nin sorduğu integral sorularından biri çok zordu, biri orta seviyeydi, biri kolaydı ve biri çok kolaydı."]},"beginTime":0,"endTime":72,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=0&ask_summarization=1"},{"index":1,"title":"İntegral Hakkında Genel Bilgiler","list":{"type":"unordered","items":["İntegral konusunu daha iyi anlamak için full tekrar videosunun üzerine bir şeyler katmak gerekebilir.","Branş denemeleri çözmek, AYT full tekrar verdiğiniz emeğin kontrol edilmesi için önemlidir.","Full tekrar sonrası soru bankalarından soru çözülebilir, AYT'e 3-4 gün kala kadar pratikler yapılabilir."]},"beginTime":72,"endTime":205,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=72&ask_summarization=1"},{"index":2,"title":"İntegral Konu Anlatımı","list":{"type":"unordered","items":["İntegral konu anlatımı belirsiz integral, diferansiyel, integral alma kuralları, belirli integral ve alan hesaplamaları gibi konuları içerecektir.","Videoda yaklaşık 30 soru sınav ayarı ve konuyu hatırlamaya yönelik, 30'dan sonrası ise sınavda üstüne çıkan sorulardan oluşacak.","İntegral, diferansiyeli bilinen bir fonksiyonun kendisini bulma işlemidir."]},"beginTime":205,"endTime":282,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=205&ask_summarization=1"},{"index":3,"title":"Diferansiyel ve İntegral İlişkisi","list":{"type":"unordered","items":["Diferansiyel, bir fonksiyonun türevini gösterir ve \"d\" harfi ile gösterilir (df(x)/dx).","Bir fonksiyonun yanına \"dx\" geldiğinde, o fonksiyonun x'e göre türevi alınmış anlamına gelir.","İntegral, bir fonksiyonun türevi alınmadan önceki haline dönmesi işlemidir ve integral sembolü ile gösterilir.","İntegral hesaplamasında \"dx\" olmadan işlem yapılamaz çünkü bir fonksiyonun türevi alınmadan önceki haline dönebilmesi için önceden türevinin alınmış olması gerekir."]},"beginTime":282,"endTime":469,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=282&ask_summarization=1"},{"index":4,"title":"İntegral ve Türev İlişkisi","list":{"type":"unordered","items":["e^x fonksiyonunun türevi e^x olur ve e^x'in integrali e^x + C olarak bulunur, burada C integral sabiti olarak adlandırılır.","İntegral sabiti (C), türev alınırken sabit sayıların sıfır olduğu için integralde her zaman eklenir.","İntegral, türevi alınmış bir fonksiyonun türevi alınmadan önceki haline dönmeyi ifade eder."]},"beginTime":474,"endTime":608,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=474&ask_summarization=1"},{"index":5,"title":"İntegral Alma Kuralları","list":{"type":"unordered","items":["İntegral alma, türev işleminin tam tersidir; türevde üstü başa geçirip bir azaltırken, integralde üstü bir artırıp başa bölme işlemi yapılır.","İntegral alma kuralı sadece x'in üstündeki fonksiyonun polinom tipi ve üssünün rasyonel sayı olması durumunda geçerlidir.","İntegral alma kuralı, üssü -1 olan fonksiyonlar için geçerli değildir çünkü bu durumda sıfır bölme hatası oluşur."]},"beginTime":608,"endTime":794,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=608&ask_summarization=1"},{"index":6,"title":"İntegralin Özellikleri","list":{"type":"unordered","items":["İntegralin en önemli özellikleri arasında sabit sayıların integralin dışına çıkabilmesi ve toplam veya fark olan fonksiyonların ayrı ayrı integral alınabilmesi bulunmaktadır.","İntegralin türevi alındığında fonksiyonun kendisi elde edilir, bu \"türev integrali götürür\" olarak ifade edilir.","İntegral ve türev birbirini götürürken, integralin içindeki bir fonksiyonun türevi alındığında +C sabiti unutulmamalıdır."]},"beginTime":794,"endTime":1053,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=794&ask_summarization=1"},{"index":7,"title":"Türev ve İntegral Uygulamaları","list":{"type":"unordered","items":["Türev-integral ilişkisi sorularında, ne zaman türev ne zaman integral alınacağı soru pratiği yaparak karar verilmelidir.","Bu tür sorularda her zaman aynı işlemi yapmak yerine, sorunun yapısına göre uygun işlem seçilmelidir.","ÖSYM'nin bu konuda soruları ezberleme yerine mantık ve pratikle çözülmelidir."]},"beginTime":1053,"endTime":1105,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1053&ask_summarization=1"},{"index":8,"title":"Belirsiz İntegralde Değişken Değiştirme","list":{"type":"unordered","items":["İntegral işaretinin altında hem fonksiyon hem de fonksiyonun türevi aynı anda bulunuyorsa değişken değiştirme kullanılır.","Örneğin, integral(f(x) çarpı f'(x) dx) alırken değişken değiştirme kullanılır çünkü integrenin içerisinde hem fonksiyonun kendisi hem de türevi var.","Değişken değiştirme yöntemiyle, integralin sonucunu e^x'in karesi bölü iki artı c şeklinde bulabiliriz."]},"beginTime":1108,"endTime":1196,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1108&ask_summarization=1"},{"index":9,"title":"Değişken Değiştirme Örnekleri","list":{"type":"unordered","items":["İntegral(x + x² + 3)⁴ çarpı 2x dx gibi sorularda da değişken değiştirme kullanılabilir.","x² + 3 = u diyerek değişken değiştirme yapılır ve integral u³ du şeklinde yazılır.","İntegralin sonucu x² + 3'in dört kuvveti bölü dört artı integral sabiti c olur."]},"beginTime":1196,"endTime":1374,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1196&ask_summarization=1"},{"index":10,"title":"Belirli İntegral","list":{"type":"unordered","items":["Belirli integralde integralin adanın bir başında a, bir diğer başında b yazılır ve bu a ve b integralin sınırlarıdır.","Belirli integralde integral sabiti yoktur, sınırlar integrali alınan fonksiyonda yerine yazılır.","Belirli integralin sonucu bir sayıdır, fonksiyon değildir."]},"beginTime":1374,"endTime":1475,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1374&ask_summarization=1"},{"index":11,"title":"Belirli İntegral Özellikleri","list":{"type":"unordered","items":["Belirli integralde integralin içindeki sabit sayı integralin dışına çıkabilir.","İntegralde alt sınırla üst sınır yer değiştirirse integral önüne bir eksi koyulur.","İntegralde sınırlar aynıysa integralin sonucu sıfırdır."]},"beginTime":1475,"endTime":1607,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1475&ask_summarization=1"},{"index":12,"title":"İntegral Özellikleri","list":{"type":"unordered","items":["Belirli integralde de ayrı ayrı toplam fark şeklinde yazılabilir.","İntegralleri aynı integralin içine almak için sınırların aynı olması gerekir.","Farklı sınırlara sahip integralleri aynı ortak integralde yazamazsınız."]},"beginTime":1607,"endTime":1667,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1607&ask_summarization=1"},{"index":13,"title":"İntegralde Parçalama","list":{"type":"unordered","items":["İntegralde, sınırlar arasında bir b sayısı seçerek integrali parçalayabilirsiniz.","Örneğin, ∫₂⁵ f(x) dx integralini, ∫₂³ f(x) dx + ∫₃⁴ f(x) dx + ∫₄⁵ f(x) dx şeklinde parçalayabilirsiniz.","İntegral parçalama işlemi özellikle alan hesaplamalarında faydalı olabilir."]},"beginTime":1678,"endTime":1754,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1678&ask_summarization=1"},{"index":14,"title":"Belirli İntegral ve Türev İlişkisi","list":{"type":"unordered","items":["Belirli integralin sonucu her zaman bir sayıdır ve bu sayının türevi sıfırdır.","Bir fonksiyonun türevinin belirli integrali, türev ve integral birbirini götürür ve sınırlar yerine yazılır.","Tek fonksiyonların eksi a'dan a'ya integrali her zaman sıfıra eşittir."]},"beginTime":1754,"endTime":1882,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1754&ask_summarization=1"},{"index":15,"title":"Çift Fonksiyonların İntegral Özellikleri","list":{"type":"unordered","items":["Çift fonksiyonlarda, 0'dan a'ya integral, -a'dan 0'a integralin iki katına eşittir.","Bu özellik bazen sorularda kullanılmaz, ancak bilinmesi faydalıdır."]},"beginTime":1882,"endTime":1907,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1882&ask_summarization=1"},{"index":16,"title":"Parçalı Fonksiyonların İntegrali","list":{"type":"unordered","items":["Parçalı fonksiyonun integralini alırken, kritik noktanın integralin sınır değerleri arasında olup olmadığına dikkat edilmelidir.","Kritik nokta sınırlar arasında ise, integral parçalanarak alınır.","Kritik nokta sınırlar dışında ise, direkt ilgili parçanın integrali alınabilir."]},"beginTime":1907,"endTime":2066,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=1907&ask_summarization=1"},{"index":17,"title":"Mutlak Değerli Fonksiyonların İntegrali","list":{"type":"unordered","items":["Mutlak değerli fonksiyonların integrali, kritik noktaya göre parçalanır ve sınır değerler değiştirilir.","Kritik nokta sınırlar arasında ise, integral parçalanır ve her parçada mutlak değer işareti kaldırılır.","Kritik nokta sınırlar dışında ise, direkt mutlak değer işareti kaldırılarak integral alınabilir."]},"beginTime":2066,"endTime":2156,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2066&ask_summarization=1"},{"index":18,"title":"Belirli İntegralde Alan Hesabı","list":{"type":"unordered","items":["İntegralin temel kullanım amacı, belirli bir eğrinin altındaki sınırlanmış alanı bulmaktır.","Eğrinin x ekseninin altında kalan alanı hesaplamak için, integral önüne eksi alınıp alan negatif çıkmaması sağlanır.","Y eksenine göre alan hesaplanırken, eğri sola doğru devrilerek integral alınır ve gerekirse integral önüne eksi alınır."]},"beginTime":2156,"endTime":2339,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2156&ask_summarization=1"},{"index":19,"title":"İki Eğri Arasındaki Alan Hesaplama","list":{"type":"unordered","items":["İki eğri arasındaki alan hesaplanırken, üstte kalan eğriden altta kalan eğri çıkarılır: ∫(f(x) - g(x))dx.","Eğer alan bir kısmı yukarıda, bir kısmı aşağıda kalıyorsa, direkt üstteki eğriden alttaki eğri çıkarılarak hesaplanabilir.","İki eğri bir noktada kesişiyorsa, kesişim noktasına göre iki ayrı integral alınır ve sonuçlar toplanır."]},"beginTime":2347,"endTime":2549,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2347&ask_summarization=1"},{"index":20,"title":"Y Eksenine Göre Alan Hesaplama","list":{"type":"unordered","items":["Y eksenine göre alan hesaplanırken de aynı mantık kullanılır: ∫(g(x) - f(x))dx.","Bir tarafı üstte, bir tarafı altta ise yine çıkararak integral sonucuna ulaşılabilir."]},"beginTime":2549,"endTime":2589,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2549&ask_summarization=1"},{"index":21,"title":"Parabolde Alan Hesaplama","list":{"type":"unordered","items":["Parabolik eğrinin altında kalan alan, üstünde kalan alanın iki katıdır.","ax³, ax⁴, ax⁵ gibi fonksiyonlar için alan hesaplamaları genelleştirilmiş bir formülle yapılır.","Ters fonksiyon ilişkisinde, alan hesaplaması için fonksiyonun tersinin integrali alınabilir."]},"beginTime":2589,"endTime":2716,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2589&ask_summarization=1"},{"index":22,"title":"Çember Yardımıyla Alan Hesaplama","list":{"type":"unordered","items":["Birim çemberin denklemi x² + y² = 1, merkezi (a,b) olan çemberin denklemi (x-a)² + (y-b)² = r²'dir.","Çemberin denklemi y = ±√(r² - x²) şeklinde yazılabilir, alan hesaplamalarında bu formül kullanılır.","Kök içerisinde kareli ifadeler verildiğinde, çember veya daire düşünülerek alan hesaplaması yapılabilir."]},"beginTime":2716,"endTime":2931,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2716&ask_summarization=1"},{"index":23,"title":"Riemann Toplamı ve Önemi","list":{"type":"unordered","items":["Riemann toplamı, integralin ilk anlatılması gereken konularından biridir ve alan hesaplamasını temsil eder.","ÖSYM denemelerinde beklenmedik sorular çıkabilir, bu nedenle Riemann toplamı soruları da denemelere dahil edilmiştir.","Riemann toplamı, bir fonksiyonun belli bir aralıkta kalan alanın hesaplanmasını sağlar."]},"beginTime":2932,"endTime":2991,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2932&ask_summarization=1"},{"index":24,"title":"Riemann Toplamı Yöntemi","list":{"type":"unordered","items":["Riemann, belirli bir aralığı (örneğin 1 ile 5 arasında) eşit veya eşit olmayan dikdörtgenlere böler ve bu dikdörtgenlerin alanlarını toplar.","Dikdörtgenlerin arasına boşluklar kalmaktadır, ancak bu dikdörtgenlerin boyutları küçültüldükçe (yani daha çok bölüntü oluşturulduğunda) boşluklar azalır ve gerçek alana yaklaşılır.","Riemann toplamı, belirli bir aralıktaki alanı dikdörtgen bölüntülere bölerek yaklaşık hesaplama yöntemidir."]},"beginTime":2991,"endTime":3167,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=2991&ask_summarization=1"},{"index":25,"title":"Alt ve Üst Toplam Metodu","list":{"type":"unordered","items":["Riemann toplamı iki farklı metodu içerir: alt toplam metodu (eğrinin altında kalan dikdörtgenlerle alan hesaplama) ve üst toplam metodu (eğrinin üstünde kalan dikdörtgenlerle alan hesaplama).","Gerçek alan, eğrinin altında kalan dikdörtgenlerle hesaplanan alan (Riemann alt toplamı) ile eğrinin üstünde kalan dikdörtgenlerle hesaplanan alan (Riemann üst toplamı) arasında yer alır.","Bölünmüş aralıklara \"bölüntü\" denir ve her bölünmüş aralığın genişliği \"delta x\" ile ifade edilir."]},"beginTime":3167,"endTime":3276,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=3167&ask_summarization=1"},{"index":26,"title":"Riemann Toplamı Hesaplama Örneği","list":{"type":"unordered","items":["Riemann alt toplamı hesaplanırken, eğrinin altında kalan dikdörtgenlerin alanları toplanır.","Riemann üst toplamı hesaplanırken, eğrinin üstünde kalan dikdörtgenlerin alanları toplanır.","Örnek hesaplamada, alt toplam 82, üst toplam ise 168 olarak hesaplanmıştır."]},"beginTime":3276,"endTime":3466,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=3276&ask_summarization=1"},{"index":27,"title":"Riemann Toplamları","list":{"type":"unordered","items":["Riemann toplamı, her bölüntünün orta noktasına göre hesaplanan toplam olarak tanımlanır.","Riemann toplamı hesaplanırken, bölüntülerin orta noktalarının fonksiyon değerleri kullanılır ve bu değerlerle dikdörtgen alanları hesaplanır.","Riemann alt toplamı 82, Riemann üst toplamı 168, Riemann toplamı ise 124 olarak hesaplanmıştır."]},"beginTime":3480,"endTime":3621,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=3480&ask_summarization=1"},{"index":28,"title":"Riemann Toplamlarının Gerçek Alanla İlişkisi","list":{"type":"unordered","items":["Gerçek alana en yakın olan Riemann toplamı, daha çok bölüntüye bölündüğünde elde edilir.","Riemann toplamı, gerçek alana yaklaşabilir ancak hiçbir zaman gerçek alandan çıkmaz.","Karşılaşılan sorularda bölüntü sayısı genellikle maksimum 3-4 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Hesaplama","list":{"type":"unordered","items":["4x'in integrali 2x², 5'in integrali 5x olarak hesaplanıyor ve sabit C ekleniyor.","f(x) = 2x² + 5x + C olarak bulunuyor.","f(1) = 10 bilgisi kullanılarak C = 3 olarak hesaplanıyor."]},"beginTime":4188,"endTime":4299,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=4188&ask_summarization=1"},{"index":33,"title":"Fonksiyon Değerinin Bulunması","list":{"type":"unordered","items":["f(3) değeri için x yerine 3 yazılıyor.","f(3) = 2(3²) + 5(3) + 3 = 36 olarak bulunuyor."]},"beginTime":4299,"endTime":4324,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=4299&ask_summarization=1"},{"index":34,"title":"Polinom Bölümü Sorusu","list":{"type":"unordered","items":["Bir P(x) polinomunun (x-3) ile bölümünden kalan soruluyor.","P(x) = ∫(4x³ + 3x² + 2x - 5) dx olarak verilmiş.","P(5) değeri için x yerine 5 yazılıp hesaplanıyor ve P(5) = 12 olarak bulunuyor."]},"beginTime":4324,"endTime":4507,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=4324&ask_summarization=1"},{"index":35,"title":"İntegral ve Türev Uygulaması","list":{"type":"unordered","items":["f'(x) = ∫(1 - (sin²x + cos²x)) dx integrali hesaplanıyor.","sin²x + cos²x = 1 olduğu için integral 1 dx oluyor ve f'(x) = x + C olarak bulunuyor.","f'(3) = 1 bilgisi kullanılarak C = -2 olarak hesaplanıyor ve f'(2) = 5 olarak bulunuyor."]},"beginTime":4507,"endTime":4588,"href":"/video/preview/568586450465180817?parent-reqid=1774011683733992-15495246318982916806-balancer-l7leveler-kubr-yp-klg-143-BAL&text=Integratedsful&t=4507&ask_summarization=1"},{"index":36,"title":"İntegral Sorusu Çözümü","list":{"type":"unordered","items":["Soruda f(-12) değerini bulmak için g(x) 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