A4-format til udskrift. - Aarhus Universitet

78 II. INTEGRATION
Volumen 1
2 π12 · 4 = 2π
1.19. Approximation ☞ [S] 5.9 Approximate integration
Figur
f(xi−1)
xi−1
f(xi)
xi
f(¯xi)
¯xi
Endepunkter - Midtpunkt- Trapez
1.20. Approximation ☞ [S] 5.9 Approximate integration
Endepunktsregler
1
2
Midtpunktsreglen
b
f(x)dx ≈
a
b
f(x)dx ≈
a
b
f(x)dx ≈
a
n
i=1
n
f(xi−1)∆x
i=1
n
f(xi)∆x
i=1
f( xi−1 + xi
)∆x
2
1.21. Approximation ☞ [S] 5.9 Approximate integration
Trapezreglen
Simpsons regel
b
f(x)dx ≈
a
b
f(x)dx ≈
a
n
i=1
n
i=1
x
(f(xi−1) + f(xi)) ∆x
2
(f(x2i−2) + 4f(x2i−1) + f(x2i)) ∆x
3
1.22. Approximation ☞ [S] 5.9 Approximate integration
Figur