Question

Найди площадь фигуры, ограниченой линиями y=-x^2, x=-1, x=1 осью ОХ

Answer 1

Ответ:

2/3

Пошаговое объяснение:

2/3

....

......

........

Answer 2

Finding the Area of the Figure

To find the area of the figure bounded by the lines y = -x^2, x = -1, x = 1, and the x-axis, we can use integration.

The figure is a region between the curve y = -x^2 and the x-axis, bounded by the vertical lines x = -1 and x = 1.

To find the area, we integrate the function y = -x^2 with respect to x, from x = -1 to x = 1.

The integral of -x^2 with respect to x is given by:

∫(-x^2) dx

Integrating this expression, we get:

∫(-x^2) dx = -(x^3)/3 + C

where C is the constant of integration.

To find the definite integral from x = -1 to x = 1, we substitute the limits of integration into the antiderivative:

∫[-1,1] (-x^2) dx = [-(1^3)/3 + C] - [-( (-1)^3)/3 + C]

Simplifying this expression, we get:

[-(1/3) + C] - [(-1/3) + C]

Since the constant of integration cancels out, we are left with:

[-(1/3) - (-1/3)] = -2/3

Therefore, the area of the figure bounded by the lines y = -x^2, x = -1, x = 1, and the x-axis is 2/3 square units.

Please let me know if there's anything else I can help you with!