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Консультация № 138913
01.06.2008, 12:27
0.00 руб.
0
1
1
здравствуйт. помогите найти площадь фигуры, ограниченной линиями:
y=x^(2)+1, y=x, y=5, x=0.
ответ, если можно, пришлите с решением.
y=x^(2)+1, y=x, y=5, x=0.
ответ, если можно, пришлите с решением.
Обсуждение
Неизвестный
01.06.2008, 15:15
общий
это ответ
Здравствуйте, Черенок Виктор Леонидович!
1)Найдем точки пересечения прямой у = 5 c параболой у = x^2 +1:
x^2 + 1 = 5
x = 2 и х = -2
и с прямой у = х:
х = 5
∫[ от 0 до 2] (x^2 + 1 - x)dx + ∫[ от 2 до 5] (5 - x)dx =
= (x^3/3 + x - x^2/2)[ от 0 до 2] + (5x -x^2/2)[ от 2 до 5] =
= 8/3 + 2 - 2 + 25 - 25/2 - 10 + 2 = 8/3 + 4.5 = 43/6
1)Найдем точки пересечения прямой у = 5 c параболой у = x^2 +1:
x^2 + 1 = 5
x = 2 и х = -2
и с прямой у = х:
х = 5
∫[ от 0 до 2] (x^2 + 1 - x)dx + ∫[ от 2 до 5] (5 - x)dx =
= (x^3/3 + x - x^2/2)[ от 0 до 2] + (5x -x^2/2)[ от 2 до 5] =
= 8/3 + 2 - 2 + 25 - 25/2 - 10 + 2 = 8/3 + 4.5 = 43/6
Форма ответа
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