The half-ordinates of a ship's water-plane, which is 80 m long, commencing from forward at equal intervals, are as follows: 0.2, 4.0, 5.0, 5.2, 5.0, 4.0, and 0.2 m respectively. Calculate the area of the water-plane using Simpson's First Rule. (16)
Reference Answer
### Objective To calculate the total area of the ship's water-plane using the provided half-ordinates and applying Simpson's First Rule for numerical integration. ### Principle of Simpson's First Rule Simpson's First Rule is a numerical method for approximating the definite integral of a function. It is used to find the area under a curve by dividing it into an even number of intervals of equal width and fitting parabolic arcs through sets of three successive ordinates. For this rule to be applicable, there must be an odd number of ordinates, which corresponds to an even number of equal intervals.
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