Интегрирование четных и нечетных функций.
Пусть f(x) – интегрируемая на промежутке [-a,a] четная функция: Тогда интеграл от f(x) в симметричных пределах равен удвоенному интегралу по половинному промежутку:
|
![](data:image/png;base64,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)
| (2)
|
| Для доказательства представим исходный интеграл в виде суммы двух интегралов:
|
![](data:image/png;base64,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)
| (3)
|
| Преобразуем первый интеграл в правой части этого равенства, выполнив подстановку x = – st:
|
![](data:image/png;base64,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)
| (4)
|
| Утверждение доказано.
Теореиа 2. Пусть f(x) – интегрируемая на промежутке [-a,a] нечетная функция: Тогда интеграл от f(x) в симметричных пределах равен нулю:
|
![](data:image/png;base64,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)
| (6)
|
| Теорема доказывается аналогичным образом:
|
![](data:image/png;base64,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)
| (7)
| 29. Дифференциальные уравнения - основные понятия: решение, порядок, обыкновенное дифференциальное, интегрирование дифференциальных уравнений, интегральная кривая. Дифференциальное уравнение 1-го порядка: общее и частное решения, начальное условие, задача Коши.
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