Question

Помогите пожалуйста очень надо)) у меня задание на зачет : найти площадь фигуры ограниченной линиями : Y=-x^2-1,Y=0,X=-1,X=2.Очень срочно пожалуйста)))

Answer 1

S=-integral (-x^2-1) dx[2 ;-1]= -x^3/3-x=-[(-8/3-2)-(-1/3+1)]=16/3 ед.кв.(минус-площадь под осью ОХ)

Answer 2

Finding the Area of the Bounded Figure

To find the area of the figure bounded by the lines Y = -x^2 - 1, Y = 0, X = -1, and X = 2, we can use the definite integral to calculate the area between the curves.

The area can be calculated by finding the integral of the top curve minus the bottom curve with respect to x, within the given bounds.

Calculating the Area

The area can be calculated using the following steps:

1. Identify the bounds of integration. 2. Determine the top and bottom curves within these bounds. 3. Set up the integral to find the area between the curves.

Solution

The bounds of integration are X = -1 and X = 2.

The top curve is Y = 0, and the bottom curve is Y = -x^2 - 1.

The integral to find the area is:

A = ∫[from -1 to 2] (0 - (-x^2 - 1)) dx

Solving the integral will give us the area of the bounded figure.

Let's calculate the integral to find the area.