Пример. Двойные числовые интегралы

Операторы > Операторы математического анализа > Пример. Двойные числовые интегралы

Вычислите интегралы вещественнозначной функции по области в плоскости x-y для расчета массы и центра массы области.

1. Задайте границы области, по которой берется интеграл. Задайте условия a < x < b и c(x) < y < d(x) для всех x.

2. Постройте область, для которой вычисляются интегралы.

Щелкните для копирования этого выражения

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3. Задайте интегрируемую вещественнозначную функцию.

Функция f(x, y) представляет плотность в точке (x, y). Она пропорциональна расстоянию от точки до начала координат.

4. Найдите массу внутри заданной области.

5. Найдите положение центра масс CoM.

6. Показать центр масс на предыдущем графике

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