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Задать вопрос экспертам

Консультация № 159561

04.02.2009, 02:05

0.00 руб.

0 1 1

Образование

Уважаемые эксперты помогите справиться вот с такой задачей:

Вычислить с помощью определенного интеграла площадь фигуры, ограниченной указанными линиями:

y=(x^2)+2; y=3

Заранее спасибо

Обсуждение

Неизвестный

04.02.2009, 12:46

общий

это ответ

Здравствуйте, Владимир1111111!
График первой функции будет параболой. ветки которой направлены вверх. Ее пересекает "сверху" прямая у=2.
Искомая площадь равна разнице площадей криволинейных трапеций, которые сверху ограничены функциями у=3 и у=x²+2
Найдем точки пересечения графиков функций. Для этого решим систему
y=x²+2;
y=3

3=x²+2
x²=1
x₁=-1
x₂=1
S=Int[-1, 1][3dx]-Int[-1, 1][(x²+2)dx]=3x[-1, 1]-(x³/3 + 2x)[-1, 1]=3(1-(-1))-(1/3*(1³-(-1)³)+2(1-(-1)))=6-(1/3*2 + 2*2)=2-2/3=4/3

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