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Консультация № 193064
10.04.2018, 12:44
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Пользуясь только определением интеграла, как предела интегральных сумм, вычислите интеграл от функции y=2x+5 по отрезку [-1;1]
Пользуясь только определением интеграла, как предела интегральных сумм, вычислите интеграл от функции y=2x+5 по отрезку [-1;1]
Обсуждение
10.04.2018, 14:39
общий
10.04.2018, 14:41
Адресаты:
Эта задача обсуждалась здесь. Автор вопроса разобрался самостоятельно... 
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.04.2018, 10:34
общий
это ответ
Здравствуйте, Smile!
Приведу свои соображения по решению задачи. Так как заданная функция непрерывна на заданном отрезке, то искомый интеграл существует. Разобьём отрезок интегрирования на
равных частей и построим полос одинаковой ширины 
Абсциссы точек разбиения таковы:
За точки
примем правые концы 
оснований 
-ых полос. Составим интегральную сумму Римана:
В соответствии с определением,
Приведу свои соображения по решению задачи. Так как заданная функция непрерывна на заданном отрезке, то искомый интеграл существует. Разобьём отрезок интегрирования на
равных частей и построим полос одинаковой ширины Абсциссы точек разбиения таковы:За точки
примем правые концы оснований -ых полос. Составим интегральную сумму Римана:В соответствии с определением,
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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