F5 math m1 trapezoidal rule(2)

2014-12-13 9:05 am

Picture: http://postimg.org/image/qx4rf4iqx/
Oil is spilled at the foot of a wall and is spreading out on the floor. The lengths of the area covered by oil at 1-cm intervals along the wall are given below:
Distance along the wall x/cm (length y/cm)
0(0.6)
1(1.3)
2(1.7)
3(2)
4(1.8)
5(1.4)
6(0)
Approximate the area covered by the oil ising the trapezoidal rule.

The question does not given any equation. Then how can i calculate the area?

Please help, thank you~

回答 (1)

知足常樂

2014-12-13 9:33 am

✔ 最佳答案

圖片參考：https://s.yimg.com/rk/HA00430218/o/1572276754.png

梯形面積 = (上底 + 下底) * 高 / 2

　(0.6 + 1.3)(1/2)
+ (1.3 + 1.7)(1/2)
+ (1.7 + 2)(1/2)
+ (2 + 1.8)(1/2)
+ (1.8 + 1.4)(1/2)
+ (1.4 + 0)(1/2)

= [0.6 + 0 + 2(1.3 + 1.7 + 2 + 1.8 + 1.4) ] (1/2)

= 8.5 cm²

2014-12-14 18:21:01 補充：
Re: 補充發問:

對於本題, 是!
無法找出這幅圖的equation來計算,
以梯形面積計算的方法似乎是你的課程內唯一的方法.
(其實還有一個叫 Simpson's rule 的東西, 但你應該不必學習)

其實本題正正旨在教導同學明白梯形法。
例如, 什麼時候適用, 如何用, 等等。

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