tF}[ΜΕIθΜΨΎ (559Ϊ½)
γΊO1-V
oπ KΑͺ―Ά°({Ζ) (Χ) ©ID Ϊ½x Ϊ[ρ
535: 07/30(
)11:29 ID:O8+PnNqB(1/3) AAS
f(t)=t (-Ξ<t?Ξ)
b_n=η_(-Ξ)^Ξ?f(t)sin(nt) dt=η_(-Ξ)^Ξ?tsin(nt) dt
=-η_(-Ξ)^Ξ??t(cos(nt)/n)^' ? dt
=-[t/n cos(nt)]_(-Ξ)^Ξ+1/n η_(-Ξ)^Ξ?cos(nt) dt
=-(Ξ/n cos(nΞ)-(-Ξ)/n cos(-nΞ))+1/n [1/n sin(nt)]_(-Ξ)^Ξ
=-(Ξ/n cos(nΞ)+Ξ/n cos(nΞ))=2Ξ (-cos(nΞ))/n=2Ξ (-1)^(n+1)/n
f(t)=2?_(n=1)^?(-1)^(n+1)/n sin(nt)
Θ4
536: 07/30(
)11:30 ID:O8+PnNqB(2/3) AAS
η_0^?(sin(x))/x dx
έ/έs (e^(-sx) (sin(x))/x)=-xe^(-sx) (sin(x))/x=-e^(-sx) sin(x)
F(s)=η_0^??e^(-sx) (sin(x))/x? dx (s?0)
dF(s)/ds=d/ds η_0^??e^(-sx) sin?(x)/x? dx
=η_0^??έ/ds e^(-sx) sin?(x)/x? dx
=η_0^??-xe^(-sx) sin?(x)/x? dx=-η_0^??e^(-sx) sin?(x) ? dx
=-η_0^??-1/s (e^(-sx) )^' sin(x)? dx
Θ7
537: 07/30(
)11:31 ID:O8+PnNqB(3/3) AAS
dF(s)/ds+1/s^2 dF(s)/ds=-1/s^2
(1+1/s^2 ) dF(s)/ds=((s^2+1)/s^2 ) dF(s)/ds=-1/s^2
dF(s)/ds=-1/(s^2+1)
F(s)=-η?1/(s^2+1) ds s=tan(Ζ) ds=1/(?cos?^2 (Ζ) ) dΖ
-η?1/(s^2+1) ds=-η??1/(?tan?^2 (Ζ)+1)?1/(?cos?^2 (Ζ) )? dΖ=-Ζ=-arctan(s)+C
F(s)=-arctan(s)+C
F(s)=η_0^??e^(-sx) sin?(x)/x? dx (s?0)
Θ3
γΊO1-VΦΚΒυέxπ
½Ϊξρ ΤΪ½o ζΪ½o πΜ’Η½Ϊ AA»ΡΘ²Ω
Κ±Μθ Κ±TOP 1.154s*