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Eğitmen önce bu hesaplama için dikkat edilmesi gereken iki temel noktayı açıklar: alanın x ekseninin üstünde mi yoksa altında mı olduğu. Ardından formülleri çizimle göstererek, alanın x ekseninin üstünde ise integral sonucunun direkt alana eşit olduğunu, altında ise integral sonucunun eksi ile çarpılarak alana eşit olduğunu açıklar. Son olarak, bu kavramları iki örnek üzerinden uygulamalı olarak gösterir."]},"endTime":587,"title":"İntegral ile X Ekseni ile Grafik Arasında Kalan Alan Hesaplama","beginTime":0}],"fullResult":[{"index":0,"title":"İntegral ile Alan Hesaplama Yöntemleri","list":{"type":"unordered","items":["İntegral yardımıyla alan bulma üç çeşittir: x ekseniyle grafik arasında, y ekseni ile grafik arasında ve iki grafik arasında kalan alan.","Bu videoda x ekseni ile grafik arasında kalan alanı bulma konusu ele alınacaktır."]},"beginTime":1,"endTime":26,"href":"/video/preview/2157611543219079617?parent-reqid=1773613303730840-1579008615794796977-balancer-l7leveler-kubr-yp-vla-146-BAL&text=CSU+Mathematics&t=1&ask_summarization=1"},{"index":1,"title":"Alan Hesaplama İçin İki Durum","list":{"type":"unordered","items":["Alan x ekseninin üstünde ise, fonksiyon sürekli pozitif değerler aldığından integral sonucu pozitif olur ve doğrudan alana eşittir.","Alan x ekseninin altında ise, fonksiyon negatif değerler aldığından integral sonucu negatif olur, bu nedenle sonucu eksi ile çarpmak gerekir."]},"beginTime":26,"endTime":175,"href":"/video/preview/2157611543219079617?parent-reqid=1773613303730840-1579008615794796977-balancer-l7leveler-kubr-yp-vla-146-BAL&text=CSU+Mathematics&t=26&ask_summarization=1"},{"index":2,"title":"Alan Hesaplama Formülleri","list":{"type":"unordered","items":["Alan x ekseninin üstünde ise: A = ∫[a to b] f(x) dx (integral sonucu doğrudan alana eşittir).","Alan x ekseninin altında ise: A = -∫[a to b] f(x) dx (integral sonucu negatif olduğu için eksi ile çarpılır)."]},"beginTime":175,"endTime":276,"href":"/video/preview/2157611543219079617?parent-reqid=1773613303730840-1579008615794796977-balancer-l7leveler-kubr-yp-vla-146-BAL&text=CSU+Mathematics&t=175&ask_summarization=1"},{"index":3,"title":"Örnek Problemler","list":{"type":"unordered","items":["Örnek 1: y = x² ve x = 4 doğrusu ile x ekseni arasında kalan alan hesaplanır ve sonuç 64 birim kare olarak bulunur.","Örnek 2: y = x³ fonksiyonu ile x ekseni arasında kalan alan, iki farklı bölgeye ayrılarak hesaplanır ve sonuç 97/4 birim kare olarak bulunur."]},"beginTime":276,"endTime":547,"href":"/video/preview/2157611543219079617?parent-reqid=1773613303730840-1579008615794796977-balancer-l7leveler-kubr-yp-vla-146-BAL&text=CSU+Mathematics&t=276&ask_summarization=1"},{"index":4,"title":"Sonuç","list":{"type":"unordered","items":["X ekseni ile grafik arasında kalan alan hesaplamasında, alanın x ekseninin hangi tarafında olduğu önemlidir.","Sorular ya grafiği çizip verilebilir ya da verbal olarak 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