GATE 2021 CE (CE1) – Question 46
For x=2.0,2.5,3.0,3.5,4.0 the ordinates are 5.00,7.25,10.00,13.25,17.00. Find area by Simpson’s 1/3 rule to two decimals.
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Correct answer: 20 to 21
Explanation
Here h=0.5 and there are four intervals. Simpson’s rule gives $A=(0.5/3)[5+17+4(7.25+13.25)+2(10)]=124/6=20.6667$. Thus **20.67** square units. Endpoints receive weight 1, odd interior ordinates 4, and the middle ordinate 2.