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$$\leq$$x$$\leq$$$$\lambda\pi$$
and f(x) = ($$\lambda$$/1-$$\lambda$$)($$\pi$$-$$\lambda$$) for $$\lambda$$$$\pi$$$$\leq$$x$$\leq$$$$\pi$$

 

[gtfitzpatrick]

show

f(x)=2/$$\pi$$(1-$$\lambda$$) $$\sum$$ (sinn$$\lambda$$$$\pi$$sinnx)/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$$\pi$$x/$$\pi$$) + 1/$$\pi$$ $$\int$$ $$^{\pi}_{\lambda\pi}$$ ---- sin(n$$\pi$$x/$$\pi$$)

 

[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$\pi$x/$\pi$) + 1/$\pi$ $\int^{pi}_{\lambda\pi}$ ($$\lambda$$/1-$$\lambda$$)($\pi$-x) sin(n$\pi$x/$\pi$)

do i work from here?