Question

Найдите площадь фигуры ограничений линиями y=-x^2+4x и y=x График тоде нужен !

Answer 1

У+x(2), то есть берём знаменатель, как в дробях. остаётся только y, умножаем как неизвестное частное на вторую линию и собираем 2+4. 2+4=как мы знаем, 6.

Answer 2

Finding the Area of the Bounded Figure

To find the area of the figure bounded by the lines \(y=-x^2+4x\) and \(y=x\), we can start by determining the points of intersection between the two curves. Once we have the points of intersection, we can calculate the area between the curves by integrating the absolute difference between the two functions over the interval of intersection.

Points of Intersection

The points of intersection can be found by setting the two functions equal to each other and solving for \(x\): \[ -x^2+4x = x \]

Solving this equation will give us the x-coordinates of the points of intersection.

Calculating the Area

Once we have the points of intersection, we can calculate the area between the curves using the formula: \[ A = \int_{a}^{b} |f(x) - g(x)| \, dx \] where \(f(x)\) and \(g(x)\) are the two functions, and \(a\) and \(b\) are the x-coordinates of the points of intersection.

Let's proceed with finding the points of intersection and calculating the area between the curves.