Finding f(x) for 0<\lambda<1: Solving for Coefficients a_n and b_n

[gtfitzpatrick]

Homework Statement

if 0<\lambda<1 and f(x) = x for 0\leqx\leq\lambda\pi
and f(x) = (\lambda/1-\lambda)(\pi-\lambda) for \lambda\pi\leqx\leq\pi

 

[gtfitzpatrick]

show

f(x)=2/\pi(1-\lambda) \sum (sinn\lambda\pisinnx)/n^{2}

 

[gtfitzpatrick]

so am i right a_{0} and a_{n} are both 0

so then is b_{n} = 1/\pi \int^{\lambda\pi}_{0} xsin(n\pix/\pi) + 1/\pi \int ^{\pi}_{\lambda\pi} ---- sin(n\pix/\pi)

 

[Defennder]

I'm not sure what you're writing here, is it \lambda \pi or \lambda^{\pi} ?

 

[gtfitzpatrick]

its (\lambda)(\pi) not powered or anything, all on the same line but came out funny sometimes, phi seem to move up a bit

 

[Vid]

Use itex instead of tex if you want math symbols to look right in the middle of a line of text.

 

[gtfitzpatrick]

so am i right a_{o} and a_{n} are both 0

so then is b_{n} = 1/\pi \int^{\lambda\pi}_{0} xsin(n\pix/\pi) + 1/\pi \int^{pi}_{\lambda\pi} (\lambda/1-\lambda)(\pi-x) sin(n\pix/\pi)

do i work from here?