Table of Contents
Advertisement
Tips for Successful Integration Calculations
When a periodic function or integration interval results in positive and
f
x
negative
(
) function values
Perform separate integrations for each cycle, or for the positive part and the
negative part, and then combine the results.
S
S
Positive
Positive
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.
f (x)
f (x)
a
a
x
x
x
x
0
0
1
1
2
2
Examples
1 1
sin 30°= 0.5
0.5 = 30° bv 1s(sin
−1
sin
sinh 1 = 1.175201194
2 2
–1
cosh
1 = 0
π /2 radians = 90°, 50 grads = 45°
3 3
(15( π ) / 2 )1G(DRG ') c(
To calculate
4 4
1N(SETUP) 7(Sci) 3
B
b
5 5
log
1000 = log 1000 = 3
10
log
16 = 4
2
To calculate ln 90 (= log
6 6
1N(SETUP) 7(Sci) 3
1.2 × 10
7 7
(1+1)
2+2
2
3
(5
)
= 15625
5
= 2
32
S
S
Negative
Negative
x
x
x
x
b
b
3
3
4
4
bv
× 2 to three significant digits (Sci 3)
e
5
B
= 1200 B
3
B ( 1 + 1 )6 2 + 2 =
= 16
B
b
b
b
∫
∫
f(x)dx =
f(x)dx =
a
a
b
b
∫
∫
f(x)dx =
f(x)dx =
a
a
b
b
∫
∫
+
+
f(x)dx
f(x)dx
x
x
x
x
4
4
wb(sinh) 1 )=
wf(cosh
v
50 1G(DRG ') d(
1i( %) 5 e* 2 =
1i( %) 5 )* 2 =
l 1000 )=
l 2 1)(,) 16 )=
& 2 e 16 =
90) to three significant digits (Sci 3)
e
1.2 * 10 6 3 =
( 5 x)1w(
16( ") 5 e 32 =
5 16( ") 32 )=
E-16
c
c
∫
∫
f(x)dx + (–
f(x)dx + (–
a
a
Positive Part
Positive Part
Negative Part
Negative Part
S
S
(
(
Positive)
Positive)
(
(
x
x
∫
∫
∫
∫
1
1
f(x)dx +
f(x)dx +
a
a
s 30 )=
−1
) 0.5 )=
1.175201194
) 1 )=
−1
r
90
) =
g
) =
i 90 )=
3
x
) =
b
b
∫
∫
f(x)dx)
f(x)dx)
c
c
S
S
Negative)
Negative)
x
x
2
2
f(x)dx + .....
f(x)dx + .....
x
x
1
1
0.5
30
0
45
2
2.97×10
2
2.97×10
3
4
4
0
4.50×10
1200
16
15625
2
2
Hide quick links:
Advertisement
Table of Contents
