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Консультация № 200891
20.05.2021, 22:02
0.00 руб.
20.05.2021, 22:24
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Інтегральне численя = интегральное исчисление(переведено на русский)
Інтегральне численя = интегральное исчисление(переведено на русский)
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Обсуждение
20.05.2021, 22:25
общий
Адресаты:
Если пишете на украинском, то пишите правильно.
Інтегральне числення
Інтегральне числення
Об авторе:
Мне безразлично, что Вы думаете о обо мне, но я рад за Вас - Вы начали думать.
Мне безразлично, что Вы думаете о обо мне, но я рад за Вас - Вы начали думать.
20.05.2021, 22:52
общий
В примере А) в числителе я бы вынес за скобки exp(3*x). Тогда сразу видно, что желательно сделать замену z=exp(3*x), в результате чего получим подынтегральное выражение:
1/3*(1+z)*dz/(4+z^2)= 1/3*dz(4+z^2) + 1/3*z*dz/(4+z^2).
Первое слагаемое практически табличный интеграл, а во втором опять делаем замену w=z^2 и из 1/3*z*dz/(4+z^2) получаем 1/6*dw / (4+w). Это теперь тоже почти табличный интеграл. Если вызывает затруднения, то сделайте для него замену y=4+w. Тогда получите 1/6*dy/y. Это уже точно табличный интеграл с коэффициентом 1/6.
В найденном интеграле выражаем все обратно через Х.
В примере В) делаем замену z=cos(x) и получаем -dz/(2 - z)^3.
Если этот интеграл вызывает затруднения, то сделайте еще одну замену w=2 - z. Получите dw/w^3. А это уже просто табличный интеграл.
Вроде бы, так.
1/3*(1+z)*dz/(4+z^2)= 1/3*dz(4+z^2) + 1/3*z*dz/(4+z^2).
Первое слагаемое практически табличный интеграл, а во втором опять делаем замену w=z^2 и из 1/3*z*dz/(4+z^2) получаем 1/6*dw / (4+w). Это теперь тоже почти табличный интеграл. Если вызывает затруднения, то сделайте для него замену y=4+w. Тогда получите 1/6*dy/y. Это уже точно табличный интеграл с коэффициентом 1/6.
В найденном интеграле выражаем все обратно через Х.
В примере В) делаем замену z=cos(x) и получаем -dz/(2 - z)^3.
Если этот интеграл вызывает затруднения, то сделайте еще одну замену w=2 - z. Получите dw/w^3. А это уже просто табличный интеграл.
Вроде бы, так.
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