Tips on Improving Integration Value Accuracy

•When a periodic function or integration interval results in positive and negative f(x) function values

Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results.

SPositive

S Negative

∫ b f(x)dx = ∫c f(x)dx + (–∫bf(x)dx)

a

 

a

 

c

 

 

 

 

 

 

 

Positive Part

Negative Part

 

 

(S Positive)

(S Negative)

•When integration values fluctuate widely due to minute shifts in the integration interval

Divide the integration interval into multiple parts (in a way that breaks areas of wide fluctuation into small parts), perform integration on each part, and then combine the results.

∫ab f(x)dx = ∫ax1 f(x)dx + ∫xx12 f(x)dx + .....+ ∫xb4 f(x)dx

Appendix

 

 

 

<#031> ∫(ln(x), 1, e) = 1

(tol specification omitted.)

<#032> ∫ (

1

, 1, 5, 1⋅10–7)= 0.8

 

2

 

 

x

 

E-35