- #1

dp182

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## Homework Statement

let f(x)={0;-2[itex]\leq[/itex]x[itex]\leq[/itex]0.

x;0[itex]\leq[/itex]x[itex]\leq[/itex]2

find a

_{0}

a

_{n}

b

_{n}

given the period is 4

## Homework Equations

a

_{0}=1/L[itex]\int[/itex]f(x)dx

a

_{n}=1/L[itex]\int[/itex]f(x)cos(n[itex]\pi[/itex]x/L)

b

_{n}=1/L[itex]\int[/itex]f(x)sin(n[itex]\pi[/itex]x/L)

## The Attempt at a Solution

so I can get a

_{0}= 1 but I run into trouble with a

_{n}. so I plug

a

_{n}=1/2[itex]\int[/itex]xcos(n[itex]\pi[/itex]x/L) for the interval 0[itex]\leq[/itex]x[itex]\leq[/itex]2 and I get the solution

=(1/n

^{2}[itex]\pi[/itex]

^{2})2xn[itex]\pi[/itex]sin(n[itex]\pi[/itex]x/2)+4cos(n[itex]\pi[/itex]x/2) then subbing in for x I get (1/n

^{2}[itex]\pi[/itex]

^{2})(4n[itex]\pi[/itex]sin(n[itex]\pi[/itex])+4cos(n[itex]\pi[/itex])-1) can anyone tell me what I am doing wrong here?