Project ForgeEngineering Mathematics
Numerical Methods
GATE 2020
Hard
Given the dataset x=[1,3,5,15,25], f(x)=[6,8,10,12,5], the value of the integral ∫1^25 f(x)dx using Simpson's 1/3rd rule is (round off to 1 decimal place)
242(± 1 accepted)
Explanation
The 5 points form two separately equally-spaced groups: (1,3,5) with h=2, and (5,15,25) with h=10. Apply Simpson's 1/3 rule to each: I1=(2/3)[6+4(8)+10]=(2/3)(48)=32. I2=(10/3)[10+4(12)+5]=(10/3)(63)=210. Total=32+210=242.
Source: GATE CH 2020 (2020)
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