Definite Integrals(Simpsons Formula) - Casio fx-3650P Programming Manual

13 Definite integrals
The value of a definite integral can be approximated by Simpsons formula,

B
h

∫
f x ( ) x d ≈ -- - f A ( )

3
A

B A –
h = ------------ -
2n
n
As becomes larger the approximation becomes better, and the limit as
infinity is consistent with the true answer.
In general, this method gives good approximations.
ON MODE MODE
？→ Ａ：？→ Ｂ：？→ Ｃ：１→ Ｄ： （Ｂ － Ａ）÷２ Ｃ → Ｍ：√ Ａ → Ｙ：Ｌｂｌ １：Ａ ＋
２ ＤＭ － Ｍ → Ｘ：Ｙ ＋４√ Ｘ → Ｙ：Ｘ ＋ Ｍ → Ｘ：Ｙ ＋２√ Ｘ → Ｙ：Ｄ ＋１→ Ｄ：Ｃ ＞
Ｄ ⇒ Ｇｏｔｏ １ ： Ｂ － Ｍ → Ｘ ： Ｙ ＋４√ Ｘ ＋√ Ｂ → Ｙ ： ＹＭ ÷３→ Ｙ ： Ｙ ＜ 105 STEP ＞
INPUT Ａ,Ｂ : interval of integration [
OUTPUT Ｙ : value of the definite integral
10
∫
x x d
Calculate
0
Prog 1
0 EXE 1
n
∑
f B ( )
+ + 4 f A
i = 1
n
:number of stripes
MODE
20
10
= ------------- - = 21.08185107
3
0 EXE
(Simpsons formula)
( ( )h )
+ 2i 1 – + 2
PRGM
COMP
1 MODE
, ] Ｃ: number of stripes
Ａ Ｂ
.
S A
S A

n 1 –

∑
( )
f A + 2ih


i = 1
n
1 1
P1 P1 P2 P3 P4 D R
P1 P1 P2 P3 P4 D R
approaches
G
G
21