Question

Вычислить площадь фигуры, ограниченной линиями. Выполнить чертеж: у = 4 – х 2, у = х + 2

Answer 1

РЕШЕНИЕ
Пределы интегрирования 
- х² + 4 = х + 2
- х² - х + 2 = 0 - квадратное уравнение.
a = - 2 и b = 1
Парабола выше прямой.
Площадь фигуры - интеграл разности функций
$S= \int\limits^a_b {x^2+x-2} \, dx = \frac{x^3}{3}+ \frac{x^2}{2}-2x$
подставили пределы интегрирования
S = 3 1/3 - (1 1/6) = 4,5
ОТВЕТ S = 4.5

Answer 2

Calculating the Area of the Figure

To calculate the area of the figure bounded by the lines, we need to find the points of intersection and then use the definite integral to find the area between the curves.

The given equations are: - y = 4 - x^2 - y = x^2

First, we need to find the points of intersection by setting the two equations equal to each other: 4 - x^2 = x^2

Solving for x: 4 = 2x^2 x^2 = 2 x = ±√2

Now, we can find the area between the curves by integrating the absolute difference of the two functions from -√2 to √2: ∫(|4 - x^2 - x^2|) dx from -√2 to √2

This will give us the area of the figure bounded by the given lines.

Note: The search results provided did not contain specific information related to the given equations for calculating the area. Therefore, the above explanation is based on mathematical principles and methods for finding the area between curves.

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