найдите площадь криволинейной трапеции, ограниченной данными линиями: y=2/x, y=0, x=2, x=8

Ответ:

The area of the trapezoid can be found using the formula:

A = (b1 + b2) * h / 2

where b1 and b2 are the lengths of the parallel sides, and h is the height.

To find the vertices, we substitute the given x-values into the equation of the lines:

y = 2/x -> x = 2: y = 2/2 = 1 -> (2,1)

-> x = 8: y = 2/8 = 1/4 -> (8,1/4)

b1 = 8 - 2 = 6

b2 = 2/x2 - 2/x1 = 2/1 - 2/1/4 = 8

h = 1 - 0 = 1

A = (6 + 8) * 1 / 2 = 7

The area of the trapezoid is 7 square units.

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