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Консультация № 177800
10.04.2010, 20:46
0.00 руб.
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7
1
Дорогие эксперты!Помогите пожалуйста!
Вычислить несобственный интеграл 1го и второго рода,показать что они расходятся.
∫(сверху +бесконечность,снизу e) e(в степени -4x)dx.
Интеграл от плюс бесконечности до экспоненты,от экспоненты в степени минус четыри икс умноженой на dx.
Заранее благодарю!
Вычислить несобственный интеграл 1го и второго рода,показать что они расходятся.
∫(сверху +бесконечность,снизу e) e(в степени -4x)dx.
Интеграл от плюс бесконечности до экспоненты,от экспоненты в степени минус четыри икс умноженой на dx.
Заранее благодарю!
Обсуждение
10.04.2010, 21:03
общий
это ответ
Здравствуйте, SKIF62.
Это называется не интеграл "от плюс бесконечности до экспоненты", а "от e до плюс бесконечности" и вычисляется он по формуле Ньютона - Лейбница для несобственных интегралов:
[$8747$]e+[$8734$]e-4xdx=(-1/4)e-4x|e+[$8734$]=0-(-1/4)e-4e=(1/4)e-4e
Это называется не интеграл "от плюс бесконечности до экспоненты", а "от e до плюс бесконечности" и вычисляется он по формуле Ньютона - Лейбница для несобственных интегралов:
[$8747$]e+[$8734$]e-4xdx=(-1/4)e-4x|e+[$8734$]=0-(-1/4)e-4e=(1/4)e-4e
5
12.04.2010, 17:47
общий
SKIF62:
Подстановка на бесконечности и есть предел:
(-1/4)e-4x|e+∞=lim(-1/4)e-4x-(-1/4)e-4e=0+(1/4)e-4e
Подстановка на бесконечности и есть предел:
(-1/4)e-4x|e+∞=lim(-1/4)e-4x-(-1/4)e-4e=0+(1/4)e-4e
12.04.2010, 17:51
общий
star9491:
Только 0+(1/4)e-4e
Только 0+(1/4)e-4e
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
Неизвестный
12.04.2010, 18:02
общий
спасибо,а то запутался немного,забыл спросить.А там сходится или рассходится?
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