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The temperature distribution T(r) at a distance r, measured from one end, along a bar of length L is given by T(x)= Kr(L-x), for

 

The temperature distribution T(r) at a distance r, measured from one end, along a bar of length L is given by T(x)= Kr(L-x), for 0xL, K = constant. (a) Express T(r) as a half-range sine series expansion. (b) Express T(r) as a half-range cosine series expansion... (c) Find the full-range Fourier series expansion of T(x).

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