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Video, bir test formatında sunulmuş olup, her soru için adım adım çözüm yöntemi gösterilmektedir."]},"endTime":619,"title":"İntegralde Alan Hesaplama Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"İntegralde Alan Kavramı","list":{"type":"unordered","items":["İntegralde alan konusu sınavda kesin soru içeren önemli bir konudur.","İntegralde alan hesaplaması kolaydan zora doğru tüm mantıklarla öğrenilir."]},"beginTime":10,"endTime":37,"href":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=10&ask_summarization=1"},{"index":1,"title":"Fonksiyonlarla Alan Hesaplama","list":{"type":"unordered","items":["Y = f(x) fonksiyonu ile x ekseni arasında kalan bölgenin alanı, -2'den 3'e kadar f(x) dx şeklinde gösterilir.","Fonksiyonun x ekseninin altında olduğu durumlarda, alan değeri integral değerinin eksi işaretlisidir.","İki eğri arasında kalan bölgenin alanı, üst kapak fonksiyonun alt kapak fonksiyondan çıkarılmasıyla hesaplanır."]},"beginTime":37,"endTime":212,"href":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=37&ask_summarization=1"},{"index":2,"title":"İntegral Değerlerinin Parçalanması","list":{"type":"unordered","items":["İntegral değerleri, aralıkların parçalanmasıyla hesaplanabilir.","Üstteki fonksiyon alttaki fonksiyondan büyükse, integral değeri alan değerine eşittir.","Üstteki fonksiyon alttaki fonksiyondan küçükse, integral değeri alan değerinin eksi işaretlisidir."]},"beginTime":212,"endTime":318,"href":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=212&ask_summarization=1"},{"index":3,"title":"Alan Değerlerinin Karşılaştırılması","list":{"type":"unordered","items":["Fonksiyonun grafiği verildiğinde, alanların değerleri integral değerleriyle ilişkilendirilebilir.","Fonksiyonun x ekseninin üstünde olduğu aralıklarda integral değeri alan değerine eşittir.","Fonksiyonun x ekseninin altında olduğu aralıklarda integral değeri alan değerinin eksi işaretlisidir."]},"beginTime":318,"endTime":437,"href":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=318&ask_summarization=1"},{"index":4,"title":"Mutlak Değer İntegrali","list":{"type":"unordered","items":["Mutlak değer integrali hesaplanırken, alttaki alanlar yukarı katlanır ve hepsi artı olur.","Mutlak değer integrali, tüm alanların toplamını verir.","İntegralde alan hesaplaması zor değildir ve temel mantıklarla öğrenilebilir."]},"beginTime":437,"endTime":618,"href":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=437&ask_summarization=1"}],"linkTemplate":"/video/preview/16603185073100234653?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Integral test 13 golden book solutions (miray publications ayt mathematics question bank)","related_orig_text":"Integral Solutions","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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Öğretmen, öğrencilere hitap ederek integral konusunu anlatmaktadır.","Video, Riemann toplamlarının uygulamalarını içeren soru çözümlerinden oluşmaktadır. İlk bölümde kapalı aralıkların alt ve üst toplamlarını hesaplama yöntemleri, fonksiyonların alt ve üst değerlerini kullanma teknikleri ve dikdörtgenlerin alanlarını hesaplama yöntemleri gösterilmektedir. İkinci bölümde ise dikdörtgenlerin alanlarını hesaplayarak integral değerlerini bulma, küp şeklindeki bir alanın hesaplanması ve parabol şeklindeki bir fonksiyonun alt ve üst toplamlarının hesaplanması gibi test soruları çözülmektedir.","Videoda toplam dokuz soru çözülmekte ve her soru için detaylı çözüm adımları verilmektedir. Sorular \"Denizli\", \"Ceyhan\" ve \"Bursa\" gibi şehir isimleriyle işaretlenmektedir. Video, sınava hazırlık amacıyla hazırlanmış test çözümlerini içermektedir."]},"endTime":982,"title":"İntegralin Uygulamaları: Riemann Toplamları ve Test Çözümleri","beginTime":0}],"fullResult":[{"index":0,"title":"Riemann Toplamı Kavramı","list":{"type":"unordered","items":["Riemann toplamı, integralin uygulamalarından önemli bir konudur.","Bir kapalı aralık, n tane kapalı alt aralığa bölündüğünde, her parçanın uzunluğu (b-a)/n olur.","Alt toplam için fonksiyonun alt değerleri, üst toplam için ise üst değerler kullanılır."]},"beginTime":8,"endTime":97,"href":"/video/preview/11507484573097764660?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=8&ask_summarization=1"},{"index":1,"title":"Riemann Toplamı Örnekleri","list":{"type":"unordered","items":["1-2 aralığında tanımlı f(x)=x fonksiyonu dört eşit aralığa bölündüğünde, her parçanın uzunluğu 1/4 olur.","Alt toplam için f(1), f(5/4), f(3/2) ve f(7/4) değerleri kullanılır.","Üst toplam için ise fonksiyonun üst değerleri kullanılır."]},"beginTime":97,"endTime":190,"href":"/video/preview/11507484573097764660?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=97&ask_summarization=1"},{"index":2,"title":"Farklı Fonksiyonlarla Riemann Toplamı","list":{"type":"unordered","items":["y=f(x) eğrisi, x=2 doğrusu ve eksenler arasında kalan bölge üç aralığa bölündüğünde, her parçanın uzunluğu 2/3 olur.","Alt toplam için f(0), f(2/3) ve f(4/3) değerleri kullanılır.","Üst toplam için ise fonksiyonun üst değerleri kullanılır."]},"beginTime":190,"endTime":323,"href":"/video/preview/11507484573097764660?parent-reqid=1769585366497141-10016549663716161466-balancer-l7leveler-kubr-yp-sas-95-BAL&text=Integral+Solutions&t=190&ask_summarization=1"},{"index":3,"title":"Üst Toplam Örnekleri","list":{"type":"unordered","items":["1-3 aralığında kalan bölge iki eşit kapalı aralığa bölündüğünde, her parçanın 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