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Консультация № 128741
23.03.2008, 19:43
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Уважаемые эксперты помогите пожайлуста решить следующие задачи по высшей математике:
1) Нужно найти несобственный интеграл следующего вида:
Знак интеграла от минус бесконечности до плюс бесконечности: в числителе dx, а в знаменателе x в квадрате + 4x +9.
Ответ будет в числителе пи умноженный на корень из 5, а в знаменателе 5. Нужно решить данный интеграл не позднее 14:00 24 марта 2008 года.
2) Нужно найти несобственный интеграл следующего вида:
Знак интеграла от Пи/2 до плюс бесконечности:2+sinx/x в квадрате умноженный на dx.
Ради всего святого это вопрос жизни и смерти, если мне никто не поможет то я умру.
Заранее спасибо.
Сообщение от Орлова Виктора Фёдоровича.
23.03.08.
1) Нужно найти несобственный интеграл следующего вида:
Знак интеграла от минус бесконечности до плюс бесконечности: в числителе dx, а в знаменателе x в квадрате + 4x +9.
Ответ будет в числителе пи умноженный на корень из 5, а в знаменателе 5. Нужно решить данный интеграл не позднее 14:00 24 марта 2008 года.
2) Нужно найти несобственный интеграл следующего вида:
Знак интеграла от Пи/2 до плюс бесконечности:2+sinx/x в квадрате умноженный на dx.
Ради всего святого это вопрос жизни и смерти, если мне никто не поможет то я умру.
Заранее спасибо.
Сообщение от Орлова Виктора Фёдоровича.
23.03.08.
Обсуждение
Неизвестный
23.03.2008, 21:56
общий
это ответ
Здравствуйте, Орлов Виктор Фёдорович!
давайте преобразуем знаменатель дроби:
x^2+4x+9=(x^2+4x+4)+5=(x+2)^2+[sqrt(5)]^2
а это у нас табличный интеграл:
инт(du/(u^2+a^2))=1/a *arctg(u/a)
у нас:
u=x+2
a=sqrt(5)
тогда получаеться что наш интеграл в общем случае равен:
1/sqrt(5) *arctg[(x+2)/sqrt(5)]
подставим вместо x + и - бессконечность, arctg плюс бесконечности равен pi/2, а минус бесконечности -pi/2
итого:
1/sqrt(5) *pi/2 - 1/sqrt(5) *(-pi/2)=pi/sqrt(5)
Приложение:
sqrt- корень квадратный
давайте преобразуем знаменатель дроби:
x^2+4x+9=(x^2+4x+4)+5=(x+2)^2+[sqrt(5)]^2
а это у нас табличный интеграл:
инт(du/(u^2+a^2))=1/a *arctg(u/a)
у нас:
u=x+2
a=sqrt(5)
тогда получаеться что наш интеграл в общем случае равен:
1/sqrt(5) *arctg[(x+2)/sqrt(5)]
подставим вместо x + и - бессконечность, arctg плюс бесконечности равен pi/2, а минус бесконечности -pi/2
итого:
1/sqrt(5) *pi/2 - 1/sqrt(5) *(-pi/2)=pi/sqrt(5)
Приложение:
sqrt- корень квадратный
Форма ответа
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