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Şarkıda \"ötme bülbül, ötme şen değil bağım dost senin derdinden ben yana yana\" sözleriyle başlayan ve \"abdal pir sultan'im\" ifadesiyle devam eden bir şarkı sunulmaktadır.","Şarkı, Pir Sultan Abdal'ın halkın sevdiği için asıldığını ve halkın derdinden yana olduğunu anlatan duygusal sözler içermektedir. Şarkıda \"feryadan ayrılmış sellere döndüm\", \"vakitsiz açılan güllere döndüm\" gibi metaforlar kullanılarak Pir Sultan Abdal'ın yaşadığı zorluklar ve halkın derdinden yana olma kararlılığı vurgulanmaktadır."]},"endTime":140,"title":"Pir Sultan Abdal Şarkısı","beginTime":0}],"fullResult":[{"index":0,"title":"Pir Sultan Abdal'ın Şarkısı","list":{"type":"unordered","items":["Bülbülün ötmesi istenmiyor çünkü dostun derdi şen değil.","Şarkıcı fitilinin tükendiğini ve yağının eridiğini söylüyor.","\"Ben yana yana\" ifadesi tekrarlanarak dostun derdinden yana olduğunu vurguluyor."]},"beginTime":20,"endTime":58,"href":"/video/preview/463785974048558102?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=20&ask_summarization=1"},{"index":1,"title":"Şarkının Devamı","list":{"type":"unordered","items":["Şarkıcı feryattan ayrılmış sellere, ateşi kararmış küllere ve vakitsiz açılan güllere döndüğünü anlatıyor.","\"Ben yana yana\" ifadesi 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Videodaki animasyon ve örnekler için: https://math.libretexts.org/Courses/M... https://www.sfu.ca/math-coursenotes/M...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3962136/92a234fe98df222a45a63c6c2d7ec491/564x318_1"},"target":"_self","position":"18","reqid":"1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=videoid:13348643955544545583","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik eğitmeni tarafından sunulan hacim hesaplama yöntemleri hakkında kapsamlı bir eğitim dersidir.","Videoda kabuk yöntemi (shell method), washer yöntemi ve disk yöntemi gibi hacim hesaplama teknikleri detaylı olarak anlatılmaktadır. Eğitmen, y ekseni etrafında döndürülen eğrilerin oluşturduğu hacimlerin hesaplanmasını, çemberin çevresi ve alanı formüllerini hatırlatarak başlayıp, çeşitli fonksiyonların döndürülmesiyle oluşan şekillerin hacim hesaplamalarını adım adım göstermektedir.","Video boyunca sinüs eğrisi, 2y = √(x-1)+2 fonksiyonu gibi örnekler üzerinden konu pekiştirilmekte ve x ekseni etrafında döndürülen şekillerin hacim hesaplamaları da ele alınmaktadır. Eğitmen, ilerleyen videolarda tüm hacim hesaplama yöntemlerinin karşılaştırılacağını belirtmekte ve video sonunda üç sayfalık bir doküman paylaşacağını söylemektedir."]},"endTime":1941,"title":"Hacim Hesaplama Yöntemleri Matematik Dersi","beginTime":0}],"fullResult":[{"index":0,"title":"Kabuk Yöntemi Tanıtımı","list":{"type":"unordered","items":["Önceki videolarda disk yöntemi ve washer metodu anlatılmış, bu videoda ise kabuk yöntemi (shell metod) ele alınacak.","Kabuk yöntemi, hacim bulmamıza olanak sağlayan bir yöntemdir ve diğer yöntemlerle karşılaştırılacak.","Bu videoda kabuk yöntemi ile ilgili karşılaşılacak tüm konular ele alınacak, ancak tüm yöntemleri kıyaslayan bir soru çözümü de yapılacak."]},"beginTime":7,"endTime":48,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=7&ask_summarization=1"},{"index":1,"title":"Y Ekseni Etrafında Döndürme","list":{"type":"unordered","items":["Y = f(x) fonksiyonunu y ekseni etrafında döndürdüğümüzde, a ile b aralığında kalan alan içi boş bir silindir oluşturur.","Bu hacim taranmaz çünkü içi boş bir alan oluşturur, bu nedenle washer metodu kullanmak iki kademeli bir işlem gerektirir.","Washer metodu ile hesaplama yaparken, y ekseninde döndürme işlemi için iki ayrı integral işlemi yapmak gerekir."]},"beginTime":48,"endTime":219,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=48&ask_summarization=1"},{"index":2,"title":"Kabuk Yönteminin Uygulanması","list":{"type":"unordered","items":["Kabuk yönteminde, a ile b aralığında bir dikdörtgen seçilir ve bu dikdörtgen y ekseni etrafında döndürülür.","Döndürme işlemi sonucunda, seçilen dikdörtgenin yarıçapı xk olan bir silindir oluşur.","Silindirin yüksekliği, seçilen xk noktasına karşılık gelen f(xk) fonksiyonunun ordinatıdır."]},"beginTime":219,"endTime":441,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=219&ask_summarization=1"},{"index":3,"title":"Silindirik Hacim Hesaplama","list":{"type":"unordered","items":["Yarıçapı x k olan çemberin çevresi 2πx k kadardır.","Sonsuz küçük kalınlıklı bir disk için, alt tabanı 2πx, yüksekliği f(x) ve kalınlığı Δx olan bir silindirik yapı oluşur.","Silindirik hacmin formülü 2πx f(x) Δx şeklinde hesaplanır ve limit alınarak a ve b aralığında 2πx f(x) dx şeklinde ifade edilir."]},"beginTime":443,"endTime":632,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=443&ask_summarization=1"},{"index":4,"title":"Örnek Problemin Çözümü","list":{"type":"unordered","items":["Y ekseni etrafında sinüs x eğrisinin 0'dan π aralığındaki döndürülmesi sonucu oluşan şeklin hacmi hesaplanmaktadır.","Her x değeri için oluşan sonsuz küçük silindirik disklerin hacimleri toplanarak tüm hacim elde edilir.","C şekli olarak adlandırılan, ortada kalan huni gibi yapı hacim hesaplamasında dikkate alınmaz çünkü boşlukta kalmıştır."]},"beginTime":632,"endTime":762,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=632&ask_summarization=1"},{"index":5,"title":"Y Ekseni Etrafında Döndürme Hacmi","list":{"type":"unordered","items":["Y sinüs x eğrisi y ekseni etrafında döndürüldüğünde oluşan diskin hacmi, 0'dan π'ye kadar 2πx sinüs x dx integrali ile hesaplanır.","İntegrasyon işlemi kısmi integrasyon yöntemiyle çözülür ve sonuç 2π² olarak bulunur.","Bu hacim, P'nin etrafında döndürülmüş bir sinüs eğrisi şeklinde bir şemsiye gibi bir şekil oluşturur."]},"beginTime":764,"endTime":946,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=764&ask_summarization=1"},{"index":6,"title":"Y Ekseni Etrafında Döndürme Örneği","list":{"type":"unordered","items":["2y = √(x-1) + 2 fonksiyonu y ekseni etrafında döndürüldüğünde oluşan hacim, washer yöntemi veya kabuk yöntemi ile hesaplanabilir.","Washer yöntemi ile hacim, 0'dan 2'ye kadar (5²-1²)π dy ve 2'den 4'e kadar (5²-((y-2)²+1)²)π dy integralleri toplamı olarak hesaplanır.","Kabuk yöntemi ile hacim, 1'den 5'e kadar 2πx√(x-1) + 2 dx integrali ile hesaplanır ve sonuç 1264π/15 olarak bulunur."]},"beginTime":946,"endTime":1314,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=946&ask_summarization=1"},{"index":7,"title":"İki Eğri Arasındaki Hacim","list":{"type":"unordered","items":["İki eğri arasındaki hacim, kabuk yöntemi ile hesaplanabilir ve formülü V = ∫[a,b] 2πf(x)g(x) dx şeklindedir.","X ekseni etrafında döndürme için kabuk yöntemi uygulandığında, x'e paralel alınan dikdörtgenlerin çevresi 2πf(y) olur ve yükseklik f(y) olarak hesaplanır.","X ekseni etrafında döndürme için hacim formülü V = ∫[a,b] 2πf(y) dy şeklindedir."]},"beginTime":1314,"endTime":1566,"href":"/video/preview/13348643955544545583?parent-reqid=1774431520847853-10800776697458891207-balancer-l7leveler-kubr-yp-klg-175-BAL&text=fathtnc&t=1314&ask_summarization=1"},{"index":8,"title":"Hacim Hesaplama Yöntemleri","list":{"type":"unordered","items":["Fonksiyon x cinsinden verilmişse, y ekseninde döndürme işlemi yapılabilir ve hacim hesaplaması için 2π∫₀¹ (2y - x) dy formülü kullanılır.","Hacim hesaplamasında yükseklik, büyük fonksiyondan küçük fonksiyon çıkarılarak bulunur ve bu durumda x = 1 değeri de çıkarılmalıdır.","Üçgensel bölgenin x = 3 etrafında döndürülmesiyle oluşan hacimde, x = 1 ile x = 3 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