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Class 4 (4th Engineer) SC&S 📅 Jun 2025

Exam Question

The half-ordinates of a ship's waterplane, which is 80m 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 waterplane 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. In naval architecture, it is used to calculate areas and volumes from a set of equally spaced ordinates. The rule is based on approximating the area under a curve by fitting parabolic arcs through sets of three consecutive ordinates.

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