Normalize the set of functions "sin, n= 1, 2, 3,...", -d < x < d п d

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Normalize the set of functions "sin, n = 1, 2, 3,..", –d < x < d
Useful constants: h= 6.62 x 10-34 J s, c = 3 x 1010 cm s', m, = 9.1 × 10-31 kg, g= 9.8 m s?
(sin ax) dx = -
-cos ax + C
a
cos ax) dx =
sin ax + C
1
|(sin'ax) dx
1
sin 2ax + C
4a
%3D
)dx D
+
sin 2ax + C
2
4a
|* sin"az) dx = -(;
-
sin 2ax -
x cos 2ax + C
4a
8a
|f cos*ax) dx = +(;
sin 2 ax +
&a
x cos 2ax + C
4a
cos 3ax
+ C
12a
3 cos ax
| (sin ax)dx
4a
* (sin ax)dx =
(a²x² - 2) cos ax
2x sin ax
+ C
a
(ax? - 2) sin ax
2x cos ax
+ C
a?
x (cos ax)dx =
Transcribed Image Text:Normalize the set of functions "sin, n = 1, 2, 3,..", –d < x < d Useful constants: h= 6.62 x 10-34 J s, c = 3 x 1010 cm s', m, = 9.1 × 10-31 kg, g= 9.8 m s? (sin ax) dx = - -cos ax + C a cos ax) dx = sin ax + C 1 |(sin'ax) dx 1 sin 2ax + C 4a %3D )dx D + sin 2ax + C 2 4a |* sin"az) dx = -(; - sin 2ax - x cos 2ax + C 4a 8a |f cos*ax) dx = +(; sin 2 ax + &a x cos 2ax + C 4a cos 3ax + C 12a 3 cos ax | (sin ax)dx 4a * (sin ax)dx = (a²x² - 2) cos ax 2x sin ax + C a (ax? - 2) sin ax 2x cos ax + C a? x (cos ax)dx =
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