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Which of the following methods is most suitable for area calculation when boundary line is irregular? 
1. Prismoidal formula   
2. Trapezoidal rule 
3. Simpson’s rule   
4. Mid-Ordinate method

1 Answer

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Best answer
Correct Answer - Option 3 : Simpson’s rule   

Explanation

For irregular boundaries, Simpson’s rule is preferred over the trapezoidal rule to calculate the given area.

According to this rule the short length of boundaries between the two adjacent ordinates is a parabolic arch.

Simpson's rule:

In order to apply Simpson's rule, the area must be divided in even number i.e., the number of offsets must be odd i.e., n term in the last offset 'On' should be odd. 

The area is given by Simpson's rule:

\(Area = \frac{d}{3}\left[ {({O_1} + {O_n}) + 4({O_2} + {O_4} + ........ + {O_{n - 1}}) + 2({O_3} + {O_5} + ......{O_{n - 2}})} \right]\)

where O1, O2, O3, .........Ois the offset

Note:

  • In case of an even number of cross-sections, the end strip is treated separately and the area of the remaining strip is calculated by Simpson's rule. The area of the last strip can be calculated by either trapezoidal or Simpson's rule.

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