UWIS, Mathe III, Serie 1
Thomas Kuster 12. August 2005
1
1.1
1.1.1 1.1.2 1.1.3
I = Z π
π
sinkxcosnx dx
= [−coskxcosnx]π−π+ Z π
π
coskxsinnx dx
= [−coskxcosnx]π−π+ [sinkxsinnx]π−π Z π
π
sinkxcosnx dx
| {z }
=I
2I = [−coskxcosnx]π−π+ [sinkxsinnx]π−π
= −coskπ
| {z }
a
cosnπ
| {z }
b
+ cos (k(−π))
| {z }
a
cos (n(−π))
| {z }
b
+ sinkπ
| {z }
c
sinnπ
| {z }
d
−sin (k(−π))
| {z }
−c
sin (n(−π))
| {z }
−d
= −ab+ab+cd−(−c)(−d) = 0
I = 0
1