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Здравствуйте, уважаемые эксперты! Прошу вас ответить на 2 следующих вопроса, готовлюсь к экзамену, не понимаю что делаю не так в этих заданиях: 1.Вычислить площадь фигуры, ограниченной линией p=6cos3x. 2. Вычислите длины дуг кривых: y=lnx ?3?x??15
Здравствуйте, kotb9 ! Условие задачи N2: Дана кривая y = ln(x) . Затребовано вычислить длину дуги на отрезке [$8730$]3 [$8804$] x [$8804$] [$8730$]15 (надеюсь, я верно понял неряшливо-написанное Вами Условие?)
Решение : Длину дуги можно вычислить по формуле : L = ab[$8747$][$8730$][1 + (y')2]·dx (см учебную статью "Как вычислить длину дуги кривой?" Ссылка1 ) здесь y' = [ln(x)]' = 1/x - производная заданной функции y = ln(x) .
Вы можете вычислять любым удобным Вам способом (на бумажке, используя Windows-калькулятор, OnLine-калькуляторы…). Я люблю вычислять в популярном приложении Маткад (ссылка2) . Маткад избавляет меня от частых ошибок. Маткад-скриншот с графиком прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ : Длина дуги равна 2,294 ед. Проверка сделана. Мой лимит времени истёк. Для решения другой Вашей задачи Правила Портала rfpro.ru рекомендуют создавать каждую задачу в отдельной консультации. см "Как правильно задавать вопросы?" rfpro.ru/help/questions#30 . =Удачи!
В первом прикреплённом файле заливкой серого цвета показана заданная фигура полностью, а во втором -- та её часть, которая получается при изменении полярного угла от нуля до 30 градусов. Площадь этой части составляет одну шестую от площади всей фигуры. Поэтому
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Ответ : Длина дуги равна 2,294 ед. Проверка сделана.
kotb9 
(ед. площади)
