Finding Fourier Series for Piecewise Function with Parameter

[gtfitzpatrick]

Homework Statement

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

show that f(x)= 2/($$\pi$$(1-$$\lambda$$))$$\Sigma$$(sin( n$$\lambda$$$$\pi$$)sin(nx)(/n$$^{}2$$

Homework Equations

The Attempt at a Solution

am i right in saying that there is only odd so ao = 0 and an = 0

and bn = 2/$$\pi$$ ($$\int^{\lambda\pi}_{0}$$ x + $$\int^{\pi}_{\lambda\pi}$$ of the second part)sin(nx)

 

[lippyka]

=2/\pi (\lambda\pi /2 + 1/2(\pi-\lambda\pi)sin(nx))= (1/\pi)(2\lambda\pi + \pi - \lambda\pi sin(nx))bn = (2/(\pi(1-\lambda))sin(n\lambda\pi)sin(nx)