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Консультация № 195389
26.04.2019, 17:21
0.00 руб.
01.05.2019, 05:30
1
2
2
Здравствуйте! У меня возникли сложности с таким вопросом: Вычислить длины дуг кривых, заданных уравнениями в прямоугольной системе координат.
y = 1 - ln cos x,
0 [$8804$] x [$8804$] [$960$]/6
y = 1 - ln cos x,
0 [$8804$] x [$8804$] [$960$]/6
Прикрепленные файлы:
Обсуждение
27.04.2019, 11:27
общий
это ответ
Здравствуйте, syndicate71rus!
Вычисляем производную:
Длина дуги находится как интеграл:
,
Подставляем
:
Мы использовали табличный интеграл:
.
Вычисляем производную:
Длина дуги находится как интеграл:
,Подставляем
:Мы использовали табличный интеграл:
.
5
27.04.2019, 13:42
общий
это ответ
Здравствуйте, syndicate71rus!
Длина дуги кривой вычисляется по формуле:
Найдем производную нашей функции
вычислим:
Тогда неопределенный интеграл получится вот таким:
Данный интеграл можно взять через универсальную тригонометрическую подстановку
В результате этой подстановки имеем:
Получается интеграл
Итак, в результате наш определенный интеграл сводится к вычислению:
Если потребуется на каком-то этапе расписать более подробно, сигнальте
Длина дуги кривой вычисляется по формуле:
Найдем производную нашей функции
вычислим:
Тогда неопределенный интеграл получится вот таким:
Данный интеграл можно взять через универсальную тригонометрическую подстановку
В результате этой подстановки имеем:Получается интеграл
Итак, в результате наш определенный интеграл сводится к вычислению:
Если потребуется на каком-то этапе расписать более подробно, сигнальте
5
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