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Daha fazlası ve ders videolarını sıralı izlemek için: https://www.khanacademy.org.tr Matematikten sanat tarihine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3282096/b0b0d89d03f8c8b4c3dbfd83d9a22062/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/BVMlXAEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"2","reqid":"1765137780616304-1447979397623433402-balancer-l7leveler-kubr-yp-klg-142-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1765137780616304-1447979397623433402-balancer-l7leveler-kubr-yp-klg-142-BAL&text=videoid:7597230032543593028","teaser":[{"list":{"type":"unordered","items":["Bu video, matematik eğitimi formatında bir ders anlatımıdır. Eğitmen, parametrik eğrilerin yay uzunluğunu hesaplama konusunu açıklamaktadır.","Video, parametrik eğrinin yay uzunluğunu hesaplama formülünü (integral a'dan b'ye karekök içinde dx/dt² + dy/dt² dt) tanıtarak başlıyor. Eğitmen, t = 0 ile t = π/2 arasında kalan eğrinin yay uzunluğunu hesaplama örneği üzerinden formülü uyguluyor ve trigonometrik özdeşlikleri kullanarak çözümü adım adım gösteriyor. Son olarak, birim çember üzerinde eğriyi görselleştirerek formülün mantığını açıklıyor ve sonucun π/2 olduğunu gösteriyor."]},"endTime":235,"title":"Parametrik Eğrinin Yay Uzunluğu Hesaplama","beginTime":0}],"fullResult":[{"index":0,"title":"Parametrik Eğrinin Yay Uzunluğu Formülü","list":{"type":"unordered","items":["T parametresine bağlı x fonksiyonunun kosinüs t'ye ve y fonksiyonunun sinüs t'ye eşit olduğu varsayılmaktadır.","T=0 ile t=π/2 arasında kalan eğrinin yay uzunluğu hesaplanacaktır.","Parametrik eğrinin yay uzunluğu formülü: ∫[a,b] √(dx/dt)² + (dy/dt)² dt şeklindedir."]},"beginTime":0,"endTime":74,"href":"/video/preview/7597230032543593028?parent-reqid=1765137780616304-1447979397623433402-balancer-l7leveler-kubr-yp-klg-142-BAL&text=Parametrik+Solusi+Integrasi&t=0&ask_summarization=1"},{"index":1,"title":"Formülün Uygulanması","list":{"type":"unordered","items":["Verilen örnekte dx/dt = -sin t ve dy/dt = cos t olarak hesaplanmıştır.","Yay uzunluğu formülü: ∫[0,π/2] √(-sin² t 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İlk olarak, x=sec(t) ve y=tan(t) parametrik denklemlerine sahip bir eğrinin (√2,1) noktasındaki teğetinin bulunması, ikinci olarak parametrik eğrilerde ikinci türevin hesaplanması ve son olarak asteroid şeklinde bir parametrik eğrinin alanının hesaplanması konuları ele alınmaktadır. Her bir soru adım adım çözülerek, parametrik eğrilerde türev alma, teğet hesaplama ve alan bulma yöntemleri gösterilmektedir."]},"endTime":1820,"title":"Parametrik Eğriler Konusu Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Parametrik Eğrilerin Teğeti","list":{"type":"unordered","items":["Parametrik eğriler için örnekler çözülecek: x = sekan t, y = tanjant t şeklinde verilen bir eğrinin √2,1 noktasındaki teğeti bulunacak.","√2,1 noktasında x = 2 ve y = 1 olduğu için sekant t = 2 ve tanjant t = 1 denklemini sağlayan t değeri π/4 olarak bulunuyor.","Parametrik eğrilerde eğim dy/dx = (dy/dt) / (dx/dt) formülü kullanılarak hesaplanır."]},"beginTime":1,"endTime":242,"href":"/video/preview/13774877356613166700?parent-reqid=1765137780616304-1447979397623433402-balancer-l7leveler-kubr-yp-klg-142-BAL&text=Parametrik+Solusi+Integrasi&t=1&ask_summarization=1"},{"index":1,"title":"Türev Hesaplamaları","list":{"type":"unordered","items":["dy/dt = tanjant t'nin t'ye göre türevi 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