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Hazırlayan: Kemal Duran (Matematik Öğretmeni) http://www.buders.com/kadromuz.html...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/228189/bada03e826a2946215c69c560bde6d03/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/nnqc_wAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"14","reqid":"1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=videoid:4213204199098599651","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında kardioid kavramını açıklayan bir öğretici içeriktir.","Video, kardioidin kutupsal denklemlerin grafiklerinin özel bir şekline verilen isim olduğunu açıklayarak başlıyor. 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Video, iki farklı kardioid örneği üzerinden (r = 1 + cosθ ve r = 1 + sinθ) çizim sürecini detaylı şekilde gösteriyor."]},"endTime":692,"title":"Kardioid Nedir ve Nasıl Çizilir?","beginTime":0}],"fullResult":[{"index":0,"title":"Kardioid Nedir","list":{"type":"unordered","items":["Kardioid, kutupsal denklemlerin grafiklerinin özel bir şekline verilen isimdir.","Kutupsal denklemler r ve theta yazı denklemlerdir; r orijine olan uzaklığı, theta ise noktanın x ekseni ile yaptığı açıyı temsil eder.","Bir kutupsal denklemin grafiği kalp şeklini verirse, bu grafiğe kardioid denir."]},"beginTime":1,"endTime":160,"href":"/video/preview/4213204199098599651?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=1&ask_summarization=1"},{"index":1,"title":"Kardioidin Çizimi","list":{"type":"unordered","items":["Kardioid çizimi için ilk adım, teta ve r'nin alacağı değerleri gösteren bir tablo üretmektedir.","Kutupsal grafik çizmek için derece değerleri (0, 90, 180, 270, 360) ve bunların kosinüs veya sinüs değerleri hesaplanır.","İkinci adım, bu noktaları analitik düzleme yerleştirmektir; r değeri orijine olan uzaklığı temsil eder."]},"beginTime":160,"endTime":183,"href":"/video/preview/4213204199098599651?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=160&ask_summarization=1"},{"index":2,"title":"Örnek Çizimler","list":{"type":"unordered","items":["r = 1 + cos(teta) denklemi için tablo oluşturulup, 0 derecede r = 2, 90 derecede r = 1, 180 derecede r = 0, 270 derecede r = 1, 360 derecede r = 2 değerleri bulunur.","r = 1 + sin(teta) denklemi için tablo oluşturulup, 0 derecede r = 1, 90 derecede r = 2, 180 derecede r = 1, 270 derecede r = 0, 360 derecede r = 1 değerleri bulunur.","Kardioid grafikleri x eksenine göre simetrik olup kalp şeklini verir."]},"beginTime":183,"endTime":685,"href":"/video/preview/4213204199098599651?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=183&ask_summarization=1"}],"linkTemplate":"/video/preview/4213204199098599651?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Calculus-II : Kardioid Nedir ve Nasıl Çizilir? 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2 videolarına değişken değiştirme yöntemiyle giriş yapıyoruz. metodu,öabt integral,öabt analiz Oynatma Listesi Linki : • Kalkülüs 2 Kalkülüs 2 Oynatma Listesi Videoları: Değişken...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/397852/55effa3e9a315bf053cbd88d37d5be82/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/40PF5gAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"15","reqid":"1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=videoid:2900491046475357600","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeni tarafından sunulan eğitim içeriğidir. Öğretmen, integral alma tekniklerinden biri olan değişken değiştirme yöntemini anlatmaktadır.","Videoda, değişken değiştirme yönteminin temel prensipleri açıklanmakta ve çeşitli örneklerle uygulamalı olarak gösterilmektedir. Öğretmen, \"ud eşittir dx\" şeklinde bir değişken değiştirme yaparak, x² + 1 üzeri 8, 3e üzeri 3x gibi zor integrallerin nasıl çözüleceğini adım adım anlatmaktadır.","Ayrıca videoda, değişken değiştirme yaparken dikkat edilmesi gereken noktalar, katsayıların ayarlanması ve farklı durumlarda (köklü ifadeler, trigonometrik fonksiyonlar) u değişkeninin nasıl seçileceği gibi konulara da değinilmektedir. Kök içindeki ifadelerin nasıl değiştirileceği ve sonucun nasıl elde edileceği detaylı olarak açıklanmaktadır."]},"endTime":963,"title":"İntegral Alma Teknikleri: Değişken Değiştirme","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral Alma Teknikleri - Değişken Değiştirme","list":{"type":"unordered","items":["İntegral alma tekniklerinden biri olan değişken değiştirme, zor integralleri çözmek için kullanılır.","Değişken değiştirme yönteminde, integralin içindeki bir ifadeyi \"u\" olarak seçip, bu ifadenin türevinin de integralin içinde görünmesi gerekir.","Köklü ifadeler, üstel ifadeler veya parantez içindeki karmaşık ifadeler genellikle \"u\" olarak seçilmeye adaydır."]},"beginTime":0,"endTime":83,"href":"/video/preview/2900491046475357600?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=0&ask_summarization=1"},{"index":1,"title":"İlk Örnek - Değişken Değiştirme Uygulaması","list":{"type":"unordered","items":["İlk örnekte, x²+1 ifadesi \"u\" olarak seçilir çünkü türevi 2x dx şeklinde integralin içinde görünür.","İntegral, 2x dx = du şeklinde yazılır ve x²+1 üzeri 8 ifadesi u üzeri 8 olarak değiştirilir.","İntegral hesaplandıktan sonra, u yerine x²+1 yazarak cevap bulunur: (x²+1)⁹/9 + C."]},"beginTime":83,"endTime":273,"href":"/video/preview/2900491046475357600?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=83&ask_summarization=1"},{"index":2,"title":"İkinci Örnek - Değişken Değiştirme Uygulaması","list":{"type":"unordered","items":["İkinci örnekte, e^(3x) ifadesi \"u\" olarak seçilir çünkü türevi 3 dx şeklinde integralin içinde görünür.","İntegral, 3 dx = du şeklinde yazılır ve e^(3x) ifadesi u olarak değiştirilir.","İntegral hesaplandıktan sonra, u yerine 3x yazarak cevap bulunur: 3e^(3x) + C."]},"beginTime":273,"endTime":447,"href":"/video/preview/2900491046475357600?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=273&ask_summarization=1"},{"index":3,"title":"Değişken Değiştirme Uygulamaları ve Özel Durumlar","list":{"type":"unordered","items":["Değişken değiştirme yönteminde, hangi ifadelerin \"u\" olarak seçileceği önemlidir; örneğin x³+1, sin(x)+4 veya tan(x)+3 gibi ifadeler tercih edilebilir.","İçerideki ifadenin türevi dışarıda aynı şekilde gelmezse, integrali çarpıp bölerek veya x² dx'i yalnız bırakarak çözüm yapılabilir.","Köklü ifadelerde, değişken olarak değiştirilen ifade kökün içindeyse, u² şeklinde yazmak akıllıca bir yöntemdir."]},"beginTime":447,"endTime":736,"href":"/video/preview/2900491046475357600?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=447&ask_summarization=1"},{"index":4,"title":"İntegral 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Ardından iki vektörün paralel olma şartını anlatıyor ve bu durumda vektörlerin koordinatlarının oranlarının eşit olması gerektiğini açıklıyor. Her iki konu için de örnek sorular çözülerek konunun uygulamalı anlatımı yapılmaktadır."]},"endTime":388,"title":"İki Vektörün Diklik ve Paralellik Şartları","beginTime":0}],"fullResult":[{"index":0,"title":"İki Vektörün Diklik Şartı","list":{"type":"unordered","items":["İki vektörün dik olma şartı, bu vektörlerin iç çarpımlarının sıfır olmasıdır.","İç çarpım hesaplanırken her bir koordinat birbiriyle çarpılır ve sonuçlar toplanır.","İki vektör birbirine dik ise iç çarpımları sıfır olur, değilse sıfırdan farklı bir değer verir."]},"beginTime":1,"endTime":75,"href":"/video/preview/3245832170487280527?parent-reqid=1769201631568117-14373066164955520780-balancer-l7leveler-kubr-yp-klg-203-BAL&text=K+Calculus&t=1&ask_summarization=1"},{"index":1,"title":"Diklik Şartı Örnekleri","list":{"type":"unordered","items":["U vektörü (2,1,-1) ve V vektörü (3,2,6) için iç çarpım hesaplandığında sonuç 2 olduğu için dik değildirler.","U vektörü (3,x,5) ve V vektörü (-2,3,7) dik ise, iç çarpım sıfır 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