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Консультация № 185919
28.04.2012, 10:12
121.87 руб.
28.04.2012, 10:43
0
13
4
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
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Помогите решить определенные интегралы,
примеры по ссылке ниже:
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Помогите решить определенные интегралы,
примеры по ссылке ниже:
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Обсуждение
28.04.2012, 10:37
общий
Выражения для интегралов в тексте вопроса не читаются.
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.04.2012, 10:45
общий
28.04.2012, 11:41
Для изображений, чтобы "нарисовались", надо давать ссылки в виде:
[ img ]https://rfpro.ru/d/8020.jpg[ /img ] (без пробелов)
[ img ]https://rfpro.ru/d/8020.jpg[ /img ] (без пробелов)
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
28.04.2012, 11:36
общий
это ответ
Здравствуйте, Денис!
Рассмотрим второй интеграл. Имеем
С уважением.
Рассмотрим второй интеграл. Имеем
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
28.04.2012, 14:53
общий
а можно по подробнее как Вы от интеграла перешли к натуральному логарифму
28.04.2012, 14:57
общий
это ответ
Здравствуйте, Денис!
1. Интегрируя по частям, получаем
[$8747$]x2cos xdx=[$8747$]x2d(sin x)=x2sin x-2[$8747$]xsin xdx=
x2sin x+2[$8747$]xd(cos x)=x2sin x+2xcos x-2[$8747$]cos xdx=x2sin x+2xcos x-2sin x+C
[$8747$]xcos xdx=[$8747$]xd(sin x)=xsin x-[$8747$]sin xdx=xsin x+cos x+C
[$8747$]cos xdx=sin x+C (это табличный интеграл)
Отсюда находим искомый интеграл
I=[(x2sin x+2xcos x-2sin x)+7(xsin x+cos x)+12sin x]|-40=
=7-(-16sin4-8cos4+2sin4+28sin4+7cos4-12sin4)=2sin4-cos4
1. Интегрируя по частям, получаем
[$8747$]x2cos xdx=[$8747$]x2d(sin x)=x2sin x-2[$8747$]xsin xdx=
x2sin x+2[$8747$]xd(cos x)=x2sin x+2xcos x-2[$8747$]cos xdx=x2sin x+2xcos x-2sin x+C
[$8747$]xcos xdx=[$8747$]xd(sin x)=xsin x-[$8747$]sin xdx=xsin x+cos x+C
[$8747$]cos xdx=sin x+C (это табличный интеграл)
Отсюда находим искомый интеграл
I=[(x2sin x+2xcos x-2sin x)+7(xsin x+cos x)+12sin x]|-40=
=7-(-16sin4-8cos4+2sin4+28sin4+7cos4-12sin4)=2sin4-cos4
5
28.04.2012, 14:59
общий
28.04.2012, 15:00
Один из интегралов, которые должен знать любой человек, изучивший интегральное исчисление:
Об авторе:
Facta loquuntur.
Facta loquuntur.
28.04.2012, 17:31
общий
это ответ
Здравствуйте, Денис!
3) Используем замену переменной. Положим x=[$8730$]5sint; dx=[$8730$]5cost*dt.
Тогда 5-x2=5-5sin2t=5cos2t; t=arcsin(x/[$8730$]5). Пересчитаем пределы интегрирования: x=0 [$8658$] t=arcsin0=0, x=[$8730$]5/2 [$8658$] t=arcsin(1/2)=[$8719$]/6.
Получаем:
3) Используем замену переменной. Положим x=[$8730$]5sint; dx=[$8730$]5cost*dt.
Тогда 5-x2=5-5sin2t=5cos2t; t=arcsin(x/[$8730$]5). Пересчитаем пределы интегрирования: x=0 [$8658$] t=arcsin0=0, x=[$8730$]5/2 [$8658$] t=arcsin(1/2)=[$8719$]/6.
Получаем:
5
28.04.2012, 17:35
общий
Адресаты:
Здравствуйте!
Вы немного ошиблись, делая подстановку (см. значение в верхнем пределе).
Вы немного ошиблись, делая подстановку (см. значение в верхнем пределе).
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