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Консультация № 185694
28.03.2012, 04:17
79.02 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Найти коэффициенты bk (k - нижний индекс) разложения в ряд Фурье по синусам функций
0, 0<=x<2
f(x) =
2, 2<=x<=6
Найти коэффициенты bk (k - нижний индекс) разложения в ряд Фурье по синусам функций
0, 0<=x<2
f(x) =
2, 2<=x<=6
Обсуждение
28.03.2012, 05:51
общий
это ответ
Здравствуйте, Aleksandrkib!
Раскладываем f(x) по системе функций
:
.
Коэффициенты разложения имеют вид
(получается из стандартной формулы, где
нечётным продолжением f(x) на левую полуось; отсюда и двойка; и, ввиду нечётности,. все чётные компоненты ряда: косинусы и 1 выпадут из разложения).
Осталось лишь посчитать интеграл:
.
Раскладываем f(x) по системе функций
:.Коэффициенты разложения имеют вид
(получается из стандартной формулы, где
нечётным продолжением f(x) на левую полуось; отсюда и двойка; и, ввиду нечётности,. все чётные компоненты ряда: косинусы и 1 выпадут из разложения).Осталось лишь посчитать интеграл:
.
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