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Консультация № 182679
30.03.2011, 20:50
51.00 руб.
30.03.2011, 23:39
0
4
3
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
помогите пожалуйста с решением примеров. Заранее спасибо!
дайте ответ с подробным решением...
помогите пожалуйста с решением примеров. Заранее спасибо!
дайте ответ с подробным решением...
Обсуждение
31.03.2011, 04:48
общий
это ответ
Здравствуйте, Посетитель - 349343!
Предлагаю решение 1 задачи.
Будут вопросы обращайтесь в минифорум.
Удачи
Предлагаю решение 1 задачи.
Будут вопросы обращайтесь в минифорум.
Удачи
31.03.2011, 09:31
общий
это ответ
Здравствуйте, Посетитель - 349343!
На третий вопрос дано неправильное решение. Этот интеграл проще всего вычислить в полярных координатах x=rcos[$966$], y=rsin[$966$]. Учитывая, что их якобиан равен r, получаем
I=[$8747$]0pi/2d[$966$][$8747$]0Rln(1+r2)rdr=
([$8747$]0pi/2d[$966$])([$8747$]0Rln(1+r2)rdr)
Вычисляем одномерные интегралы. Первый интеграл элементарный
[$8747$]0pi/2d[$966$]=pi/2
второй интеграл берется заменой переменной u=1+r2 и интегрированием по частям
[$8747$]0Rln(1+r2)rdr=(1/2)[$8747$]11+R^2ln(u)du=
(1/2)(uln(u)-u)11+R^2=(1/2)[(1+R2)ln(1+R2)-R2]
таким образом
I=(pi/4)[(1+R2)ln(1+R2)-R2]
На третий вопрос дано неправильное решение. Этот интеграл проще всего вычислить в полярных координатах x=rcos[$966$], y=rsin[$966$]. Учитывая, что их якобиан равен r, получаем
I=[$8747$]0pi/2d[$966$][$8747$]0Rln(1+r2)rdr=
([$8747$]0pi/2d[$966$])([$8747$]0Rln(1+r2)rdr)
Вычисляем одномерные интегралы. Первый интеграл элементарный
[$8747$]0pi/2d[$966$]=pi/2
второй интеграл берется заменой переменной u=1+r2 и интегрированием по частям
[$8747$]0Rln(1+r2)rdr=(1/2)[$8747$]11+R^2ln(u)du=
(1/2)(uln(u)-u)11+R^2=(1/2)[(1+R2)ln(1+R2)-R2]
таким образом
I=(pi/4)[(1+R2)ln(1+R2)-R2]
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