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Консультация № 182354
01.03.2011, 20:08
52.69 руб.
0
10
2
Здравствуйте! Прошу помощи в следующем вопрос:
Найти площадь фигуры, ограниченной линиями: y=3+2x-x^2 и y=0
Найти площадь фигуры, ограниченной линиями: y=3+2x-x^2 и y=0
Обсуждение
01.03.2011, 20:27
общий
это ответ
Здравствуйте, Посетитель - 358526!
График первой кривой - парабола с ветвями, направленными вниз. Корни квадратого уравнения 3+2x-x2=0 равны -1 и 3. Поэтому искомая площадь равна интегралу от первой функции в пределах от -1 до 3:
S=[$8747$]-13(3+2x-x2)dx=[3x+x2-(x3/3)]-13=(9+9-9)-(-3+1+1/3)=32/3
График первой кривой - парабола с ветвями, направленными вниз. Корни квадратого уравнения 3+2x-x2=0 равны -1 и 3. Поэтому искомая площадь равна интегралу от первой функции в пределах от -1 до 3:
S=[$8747$]-13(3+2x-x2)dx=[3x+x2-(x3/3)]-13=(9+9-9)-(-3+1+1/3)=32/3
5
Неизвестный
01.03.2011, 20:33
общий
01.03.2011, 21:28
это ответ
Здравствуйте, Посетитель - 358526!
1) точки пересечения параболы y=3+2x-x^2 с ох:
3+2x-x^2 = 0
х=-1; х=3
= 3x+x^2-(x^3)/3 (от -1 до 3)
= (9+9-9) - (-3+1+1/3) = 10 2/3
1) точки пересечения параболы y=3+2x-x^2 с ох:
3+2x-x^2 = 0
х=-1; х=3
= 3x+x^2-(x^3)/3 (от -1 до 3)= (9+9-9) - (-3+1+1/3) = 10 2/3
4
01.03.2011, 20:41
общий
Здравствуйте!
По-моему, Вы упустили в подынтегральном выражении dx. И Ваша интерпретация формулы Ньютона-Лейбница представляется необычной (вряд ли правильно писать "от -1 до 3").
С уважением.
По-моему, Вы упустили в подынтегральном выражении dx. И Ваша интерпретация формулы Ньютона-Лейбница представляется необычной (вряд ли правильно писать "от -1 до 3").
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
01.03.2011, 20:43
общий
Вы правы, просто пытаюсь научиться пользоваться формулами. Забыла поставить dx. Прошу прощения
01.03.2011, 20:50
общий
С этим разобрались. А как насчёт второго замечания?
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
01.03.2011, 21:01
общий
я не знаю как поставить с помощью формулы пределы интегрирования
01.03.2011, 21:06
общий
Посмотрите, пожалуйста, как это делает автор первого ответа.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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