12
Definite Integrals
Approximations of the value of definite integrals may be obtained as follows:
B
h
∫
x ( ) x d
≈
-- - f A ( )
(
+
2
A
h
=
n
For larger
the approximation improves, and as
tends to infinity it agrees with the precise value of
the definite integral.
ON
MODE
MODE
?→ A:?→ B:?→ C:1→ D: (√ A)÷2→ Y:Lbl 1: (A(C - D)+ DB)
÷ C → X:Y +(√ X)→ Y:D +1→ D:D ≠ C ⇒ Goto 1:Y +(√ B)÷2→
Y: (B - A)Y ÷ C → Y:Y < 89 STEP >
INPUT
A,B : interval of integration [
OUTPUT
Y : value of the definite integral
Calculate the value of the definite integral
Prog
1
0
EXE
(
)
(
2f A
+
h
+
2f A
+
B A
–
------------ -
n
:number of trapezoids
n
PRGM
MODE
(Trapezoidal rule)
...
)
(
2h
+
+
2f B h
–
n
COMP
1
1
MODE
,
] C: number of trapezoids
A
B
10
20
10
∫
x x d
=
------------- -
3
0
S A
S A
)
f B ( )
)
+
a
1
=
21.08185107
.
P1 P1 P2 P3 P4
D R
P1 P1 P2 P3 P4
D R
b
G
G
19
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