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## Homework Statement

Find the solution of the heat conduction problem:

100U

_{x}

_{x}=U

_{t}, 0<x<1, t>0;

U(0,t)=0, U(1,t)=0, t>0;

U(x,0)=sin(2[tex]\pi[/tex]x)-sin(5[tex]\pi[/tex]x), 0[tex]\leq[/tex]x[tex]\leq[/tex]1

## Homework Equations

U(x,t)=[tex]\sum[/tex]c

_{n}e

^{(-n2[tex]\pi[/tex]2[tex]\alpha[/tex]2t)/L2}sin((n[tex]\pi[/tex]x)/L)

(sum from n=1 to infinity)

c

_{n}=2/L [tex]\int[/tex]f(x)sin((n[tex]\pi[/tex]x)/L)dx (evalutated from 0 to L)

## The Attempt at a Solution

c

_{n}=2[tex]\int[/tex](sin(2[tex]\pi[/tex]x)-sin(5[tex]\pi[/tex]x))sin(n[tex]\pi[/tex]x)dx=0 (evalutated from 0 to 1)

I did this tedious integral by hand and got zero and verified it with my calculator. Therefore, I think that I am setting up the problem wrong. So if this is not how to set up c

_{n}then what should I do different?

Thank you for your time.

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