Integration by parts 425
- In determining a Fourier series to repre-
sentf(x)=xin the range−πtoπ, Fourier
coefficients are given by:
an=
1
π
∫π
−π
xcosnxdx
and bn=
1
π
∫π
−π
xsinnxdx
where n is a positive integer. Show by
using integration by parts thatan=0and
bn=−
2
n
cosnπ.
- The equationC=
∫ 1
0
e−^0.^4 θcos1. 2 θdθ
and S=
∫ 1
0
e−^0.^4 θsin1. 2 θdθ
are involved in the study of damped
oscillations. Determine the values of C
andS.
[C= 0 .66,S= 0 .41]