Получим формулу прямоугольников. Для этого основание криволинейной трапеции аАВb разделим на n равных частей , т.е. длина основания каждого прямоугольника равна ∆Х. Площадь прямоугольника равна произведению основания на высоту (высота = f(xi) ; основание ∆Х )
. рис.1
(1) называется формулой прямоугольников с недостатком. На рисунке (1) очевидно, что площадь криволинейной трапеции состоит из суммы площадей прямоугольников (прямоугольники закрашены разными цветами) и неокрашенных криволинейных треугольников, площади которых мы теряем при вычислении. Или формулу (1) можно записать следующим образом (2)
Рассмотрим 2 случай (ступенчатая фигура – описанная, а значит ее площадь будет больше площади криволинейной трапеции аАВb - рисунок 2). Поступим аналогично, а именно вычислим площадь каждого прямоугольника и найдем их сумму, т.е.
рис. 2
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) (3), где – Формулу (3) называют формулой прямоугольников с избытком
или формулу (3) можно кратко записать так: (4)
Do'stlaringiz bilan baham: |