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Question

By Simpson's rule, the value of 21dxx dividing the interval (1,2) into four equal parts, is

A
0.6932
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B
0.6753
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C
0.6692
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D
7.1324
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Solution

The correct option is B 0.6932
h=214=14
Now, x0=1,x1=1+14,x2=1+2×14,x3=1+3×14,x4=1+4×14
i.e, x0=1,x1=1.25,x2=1.5,x3=1.75,x4=2
y0=1,y1=0.8,y2=0.667,y3=0.571,y4=0.5
Using Simpson's 13rd rule
21dxx=112[(1+0.5)+4(0.8+0.571)+2(0.667)]
=112[1.5+5.484+1.334]
=112[8.318]=0.6932

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