Question

The method of area calculation which is more useful when the boundary line departs considerably from the straight line is called
1. The average ordinate rule
2. Simpson's one-third rule
3. The trapezoidal rule
4. The mid-ordinate rule

Answer 1

Correct Answer - Option 2 : Simpson's one-third rule

Explanation:

Simpson's one-third rule:

This rule is based on the assumption that the figures are trapezoids.

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. 

This method of area calculation is more useful when the boundary line departs considerably from the straight line.

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, .........On is the offset

• 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.