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Консультация № 190869
12.04.2017, 15:53
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Здравствуйте! Прошу помощи в следующем вопросе:
Прикрепленные файлы:
Обсуждение
13.04.2017, 11:23
общий
это ответ
Здравствуйте, abigail!
Кривая, заданная в условии задачи системой уравнений, является не циклоидой, а эллипсом. Она показана на рисунке ниже красным цветом. Прямая
показана синим цветом. Масштабы по осям на рисунке разные. Требуется вычислить площадь фигуры, ограниченной сверху указанной прямой, а снизу эллипсом.
Если
то 
Если 
то 
Вычислим площадь фигуры, ограниченной сверху эллипсом, а снизу осью абсцисс.
(ед. площади).
Если
то 
Если 
то 
Вычислим площадь фигуры, ограниченной сверху эллипсом, а снизу прямой 
учитывая, что эта прямая пересекает эллипс в точках 
а площадь прямоугольника, вершинами которого являются эти точки и их проекции на ось абсцисс, составляет 
(ед. площади).
(ед. площади).
Искомая площадь составляет
(ед. площади).
Кривая, заданная в условии задачи системой уравнений, является не циклоидой, а эллипсом. Она показана на рисунке ниже красным цветом. Прямая
показана синим цветом. Масштабы по осям на рисунке разные. Требуется вычислить площадь фигуры, ограниченной сверху указанной прямой, а снизу эллипсом.Если
то Если то Вычислим площадь фигуры, ограниченной сверху эллипсом, а снизу осью абсцисс. (ед. площади).Если
то Если то Вычислим площадь фигуры, ограниченной сверху эллипсом, а снизу прямой учитывая, что эта прямая пересекает эллипс в точках а площадь прямоугольника, вершинами которого являются эти точки и их проекции на ось абсцисс, составляет (ед. площади). (ед. площади).Искомая площадь составляет
(ед. площади).
Об авторе:
Facta loquuntur.
Facta loquuntur.
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