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Video, matematiksel integral hesaplamalarını öğrenmek isteyenler için kapsamlı bir rehber niteliğindedir."]},"endTime":710,"title":"Gamma 1/2 Değerinin Hesaplanması","beginTime":0}],"fullResult":[{"index":0,"title":"Gamma Fonksiyonu ve Gamma","list":{"type":"unordered","items":["Video, gamma buçuk değeri nasıl hesaplanır konusunu inceleyecek.","Gamma fonksiyonu, sıfırdan sonsuza e üzeri eksi t çarpı t üzeri x bir dt integraline karşılık gelir.","Gamma buçuk hesaplanırken x yerine 1/2 yazılır ve integral sıfırdan sonsuza e üzeri eksi t çarpı t'nin eksi 1/2 kuvveti dt şeklinde yazılır.","Bu integral direkt hesaplanamaz."]},"beginTime":11,"endTime":39,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=11&ask_summarization=1"},{"index":1,"title":"İntegral Dönüşümleri ve Gamma Fonksiyonu","list":{"type":"unordered","items":["İntegralde t gördüğümüz yere x² yazarak, dt = 2x dx dönüşümü yapılıyor.","İntegral sınırları t için sonsuz, x için de sonsuz olarak belirleniyor.","İntegral sonucunda e üzeri eksi x kare dx ifadesi elde ediliyor ve bu ifade gamma 2'nin sonucu olarak bulunuyor."]},"beginTime":42,"endTime":86,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=42&ask_summarization=1"},{"index":2,"title":"İntegralin Çarpımı ve Kare İntegrali","list":{"type":"unordered","items":["İntegral I olarak adlandırılıyor ve 2x'den sonsuza e üzeri eksi y kare dy şeklinde de yazılabilir.","İki I ifadesinin çarpımı alınarak kare integral I² hesaplanıyor.","Kare integral sonucunda 4 çarpı sıfırdan sonsuza e üzeri eksi (x²+y²) dydx ifadesi elde ediliyor."]},"beginTime":86,"endTime":153,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=86&ask_summarization=1"},{"index":3,"title":"Kare İntegralin Birinci Çözüm Yöntemi","list":{"type":"unordered","items":["Kare integralin çözümünde y = xt dönüşümü yapılıyor ve dy = xdt olarak yazılıyor.","İntegral sınırları t için 0'dan sonsuza, x için de 0'dan sonsuza olarak belirleniyor.","İntegral sonucunda 4 çarpı sıfırdan sonsuza e üzeri eksi (x²+t²) dx dt ifadesi elde ediliyor."]},"beginTime":153,"endTime":227,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=153&ask_summarization=1"},{"index":4,"title":"İntegralin İkinci Çözüm Yöntemi","list":{"type":"unordered","items":["İntegralde u = x²(1+t²) dönüşümü yapılıyor ve dx = 2(1+t²) du olarak yazılıyor.","İntegral sonucunda 2 çarpı sıfırdan sonsuza e üzeri eksi u du ifadesi elde ediliyor.","İntegral sonucunda 2 çarpı arctanjant sonsuz - arctanjant 0'dan π/2'ye kadar olan integral hesaplanıyor ve sonucu π olarak bulunuyor."]},"beginTime":227,"endTime":448,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=227&ask_summarization=1"},{"index":5,"title":"Kutupsal Koordinat Dönüşümü","list":{"type":"unordered","items":["İntegralde x²+y² ifadesi için kutupsal koordinat dönüşümü yapılıyor: x = r cos θ, y = r sin θ.","Jakobian matrisi r olarak hesaplanıyor ve integral sınırları 0'dan π/2'ye, r için 0'dan sonsuza olarak belirleniyor.","İntegral sonucunda 2 çarpı π/2 = π olarak bulunuyor."]},"beginTime":448,"endTime":677,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=448&ask_summarization=1"},{"index":6,"title":"Sonuç ve Gamma Fonksiyonu","list":{"type":"unordered","items":["Hem birinci hem ikinci yoldan integralin sonucu π olarak bulunuyor.","I² = π olduğundan, I = √π olarak hesaplanıyor.","Gamma 1/2 ifadesi I integraline karşılık geldiği için, her iki tarafın karekökü alınarak gamma 1/2 = √π olarak bulunuyor."]},"beginTime":677,"endTime":702,"href":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=677&ask_summarization=1"}],"linkTemplate":"/video/preview/7113085839791637631?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Gamma bir bölü iki (1/2) nin hesaplanması, Gamma Fonksiyonu Örnek Soru, Gamma 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Defense and Banking exam on Doubtnut App or You can Whatsapp us at - 8400400400 Link - https://doubtnut.app.link/2um0jr7Joeb Join our courses to improve your performance and Clear your...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3324529/713d801c8e53b615e508e4dc91831045/564x318_1"},"target":"_self","position":"1","reqid":"1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DRJw6GK5B0X8","linkTemplate":"/video/preview/9670750507832825216?parent-reqid=1769786936408553-6636422659732507319-balancer-l7leveler-kubr-yp-klg-264-BAL&text=Gamma_B&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Arrange in increasing order of: a. 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