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MATHEMATICS - CASE STUDY

    Introduction


UFO Attack the Wheat Field
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One early morning, Jack discovered a mysterious large kidney-shaped formation in his wheat field. He was surprised and realized that he needed to estimate his wheat loss in that region.

What is known:

Jack measured at 1-foot intervals as indicated in the following figure.

y0
1.5
y5
4.4
y10
3.8
y1
3.5
y6
3.5
y11
3.5
y2
4.8
y7
2.4
y12
1.5
y3
5.3
y8
3.1
y4
5.0
y9
3.6
     
    Questions

 

  Determine the area of the kidney-shaped formation using the Midpoint Rule, Trapezoidal Rule, and Simpson's Rule.
     
    Approach


 
  • Midpoint Rule
    Area = Δx(y0 + y1 + y2 + ... + y12)
  • Trapezoidal Rule
    Area = Δx/2(y0 + 2y1 +2 y2 + ... + 2y11+ y12)
  • Simpson's Rule
    Area = h/3(y0 + 4y1 +2 y2 + ... + 4y11+ y12)