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Консультация № 84333
26.04.2007, 16:24
0.00 руб.
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Здравствуйте!
Подскажите пожалуйста с чего начать решения примера: интеграл (sin2x/cos(2^-1)x)dx
И еще маленький вопросик, если в условии задачи написано: "найти первообразную, проходящую через точку (а;в)", то есть это найти первообразную и подставить значения и найти константу С, правильно я понимаю?
Подскажите пожалуйста с чего начать решения примера: интеграл (sin2x/cos(2^-1)x)dx
И еще маленький вопросик, если в условии задачи написано: "найти первообразную, проходящую через точку (а;в)", то есть это найти первообразную и подставить значения и найти константу С, правильно я понимаю?
Обсуждение
Неизвестный
27.04.2007, 12:01
общий
это ответ
Здравствуйте, Zhiriki.
Напомню формулы sin и cos двойного угла:
sin(2 x) = 2 sin(x) cos(x) ,
cos(2 x) = 2 (cos(x))^2 - 1 .
С помощью этих формул подынтегральное выражение можно преобразовать так:
sin(0.5 x) sin(2 x) / [sin(0.5 x) cos(0.5 x)] =
= 4 sin(0.5 x) sin(x) cos(x) / sin(x) =
= 4 sin(0.5 x) (2 (cos(0.5 x))^2 - 1) .
Теперь можно sin(0.5 x) внести под знак дифференциала:
sin (0.5 x) dx = - 2 d[cos (0.5 x)] ,
а cos(0.5 x) заменить на новую переменную, например на t. Остаётся найти интеграл выражения
- 8 (2 t^2 - 1) dt .
Напомню формулы sin и cos двойного угла:
sin(2 x) = 2 sin(x) cos(x) ,
cos(2 x) = 2 (cos(x))^2 - 1 .
С помощью этих формул подынтегральное выражение можно преобразовать так:
sin(0.5 x) sin(2 x) / [sin(0.5 x) cos(0.5 x)] =
= 4 sin(0.5 x) sin(x) cos(x) / sin(x) =
= 4 sin(0.5 x) (2 (cos(0.5 x))^2 - 1) .
Теперь можно sin(0.5 x) внести под знак дифференциала:
sin (0.5 x) dx = - 2 d[cos (0.5 x)] ,
а cos(0.5 x) заменить на новую переменную, например на t. Остаётся найти интеграл выражения
- 8 (2 t^2 - 1) dt .
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