Question

Найдите площадь фигуры,ограниченной линиями y=1/x; x=2, y=2 ???

Answer 1

Решение смотри на фотографии

Answer 2

Calculating the Area of the Bounded Figure

To find the area of the figure bounded by the lines y=1/x, x=2, and y=2, we can use the definite integral to calculate the area under the curve. The area can be calculated by integrating the function y=1/x from x=1 to x=2 and subtracting the area of the triangle formed by the lines x=2, y=2, and the x-axis.

The integral to find the area under the curve y=1/x from x=1 to x=2 is:

A = ∫[1 to 2] (1/x) dx

The area of the triangle formed by the lines x=2, y=2, and the x-axis can be calculated using the formula for the area of a triangle: A_triangle = (1/2) * base * height

Let's calculate the area using the given information.

Calculating the Area Under the Curve

The integral to find the area under the curve y=1/x from x=1 to x=2 is: A = ∫[1 to 2] (1/x) dx

Using the definite integral, we can calculate the area under the curve y=1/x from x=1 to x=2.

Calculating the Area of the Triangle

The area of the triangle formed by the lines x=2, y=2, and the x-axis can be calculated using the formula for the area of a triangle: A_triangle = (1/2) * base * height

Let's calculate the area of the triangle using the given information.

Solution

The area under the curve y=1/x from x=1 to x=2 can be calculated as follows: A = ∫[1 to 2] (1/x) dx

The area of the triangle formed by the lines x=2, y=2, and the x-axis is: A_triangle = (1/2) * 1 * 2 = 1

Using the definite integral, the area under the curve y=1/x from x=1 to x=2 is found to be ln(2).

Therefore, the total area of the figure bounded by the lines y=1/x, x=2, and y=2 is: A_total = ln(2) - 1

So, the area of the figure is ln(2) - 1.