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NWDA JE CE 2019 Official Paper

Option 1 : Simpson’s

__Explanation__

(i) For irregular boundaries or curve boundary, Simpson’s rule is preferred over the trapezoidal rule to calculate the given area.

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

__Important Points__

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, .........On is the offset

Note:

(i) 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.