There are two problems written in the image, both are irregular sections. These problems can be solved using Trapezoidal Rule or Simpson’s Rule, as elaborated in the solution section below.
Problem: Determine the area enclosed between the irregularly bounded figure.
Solution:
P.2
(i)As per the Trapezoidal Rule, Area A = 10/2* {15.3 + 26.9 + 2( 12.5+17.1+28.8+32.6)} = 5 * 224.2 = 1121 sqft.
(ii) As per the Simpson’s Rule, the number of ordinates must be odd, so divide area into two parts, A1 from 1st to 5th ordinate, and A2 from 5th to 6th.
Area A1 using Simpson’s Rule, A1 = 10/3*{15.3+32.6+4(12.5+28.8) + 2(17.1)} = 824.33 sqft.,
Area A2 using Trapezoidal rule, A2 = 10/2(32.6+26.9) = 297.5 sqft
Total area, A = A1+A2 = 824.33+297.5 = 1121.83 sqft.
P.3
Use Simpson’s Rule because the number of ordinates are odd. Note that Simpson’s Rule is more accurate than the Trapezoidal rule.
A = 23/3{14.2+18.3 + 4( 18.1 + 17.6) + 2(16.7)} = 1600.033 sqft.
