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E-16
Tips for Successful Integration Calculations
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.
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.
Examples
sin 30°= 0.5 1B Q 30 0.5
sin
−1
0.5 = 30° 1B Q(sin
−1
) 0.5 30
sinh 1 = 1.175201194 @@(sinh) 1 1.175201194
cosh
–1
1 = 0 @D(cosh
−1
) 1 0
P/2 radians = 90°, 50 grads = 45° B
(P) 2 (DRG)A(
r
) 90
50 (DRG)B(
g
) 45
To calculate e
5
s2 to three significant digits (Sci 3)
(SETUP)(Sci)
2() 5 C 2
2.97×10
2
1 2() 5 2 2.97×10
2
log
10
1000 = log 1000 = 3 5 1000 3
log
2
16 = 4 5 2 (,) 16 4
2 C 16 4
To calculate ln 90 (= log
e
90) to three significant digits (Sci 3)
(SETUP)(Sci) 2 90
4.50×10
0
1.2 s10
3
= 1200 1.2 10 3 1200
(1+1)
2+2
= 16 1 1 2 2 16
(5
2
)
3
= 15625 5 V7(x
3
) 15625
32
5
= 2 () 5 C 32 2
1 5() 32 2
S Positive
S
Negative
S Positive
S
Negative
a
b
f(x)dx =
a
c
f(x)dx + (–
c
b
f(x)dx)
Positive Part
(S Positive)
Negative Part
(S Negative)
a
b
f(x)dx =
a
c
f(x)dx + (–
c
b
f(x)dx)
Positive Part
(S Positive)
Negative Part
(S Negative)
b
a
x
1
x
2
x
3
x
4
x
0
f (x)
b
a
x
1
x
2
x
3
x
4
x
0
f (x)
a
b
f(x)dx =
a
x
1
f(x)dx +
x1
x
2
f(x)dx +
.....
x4
b
f(x)dx
+
a
b
f(x)dx =
a
x
1
f(x)dx +
x1
x
2
f(x)dx +
.....
x4
b
f(x)dx
+
11
22
33
44
55
66
77