Simpson Rule Watch

Joel Brown
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#1
Report Thread starter 2 years ago
#1
Using Simpson's area rule, calculate the area of earth to be excavated given the integral:

b

f(x)dx

a

Where a=1, b=5, and f(x)=1/x^2

do this using 8 intervals

5-1/8 = 0.5


1
1.5
2
2.5
3
3.5
4
4.5
51
0.444
0.25
0.16
0.111
0.082
0.063
0.049
0.04

1 + 0.04 = 1.04
0.444 + 0.16 + 0.082 + 0.49 x 4 = 2.94
0.25 + 0.111 + 0.063 x 2 = 0.848

1/3 x 0.5 [1.04 + 2.94 + 0.848] = 0.805 to 3dp





Is this correct? or should I divide the intervals by
2/√x
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ghostwalker
  • Study Helper
Badges: 16
#2
Report 2 years ago
#2
(Original post by Joel Brown)

Is this correct? or should I divide the intervals by
2/√x
It's correct to within rounding errors. I would do intermediate work to 4dec.pl. if you're going to quote the result to 3 dec.pl. BUT go with whatever you've been taught.

Value, via Simpson is 0.800433

Actual integrated value is 0.8
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