A function of period 2L has the form i) Compute the Fourier series for this function....

Transcribed Image Text:

A function of period 2L has the form i) Compute the Fourier series for this function. ii) By choosing an appropriate value of x show that an infinite series can be con- structed for . The following indefinite integrals might be useful. (17x) dx (172) dx L n73 J J J x COS x sin x sin J X COS (nt.) dx f(x) = Lx, xe [-L, L]. X (17) dx L = = L n3 = L n L sin NTX L (L cos (17) 2LnTx cos - NTX COS :)) + L n (2Lnxx sin (T) + (2L nx) cos (17)) + nx sin L + C (27)) - L + C + C (27) - (2L nnx) sin ()) + + C. L A function of period 2L has the form i) Compute the Fourier series for this function. ii) By choosing an appropriate value of x show that an infinite series can be con- structed for . The following indefinite integrals might be useful. (17x) dx (172) dx L n73 J J J x COS x sin x sin J X COS (nt.) dx f(x) = Lx, xe [-L, L]. X (17) dx L = = L n3 = L n L sin NTX L (L cos (17) 2LnTx cos - NTX COS :)) + L n (2Lnxx sin (T) + (2L nx) cos (17)) + nx sin L + C (27)) - L + C + C (27) - (2L nnx) sin ()) + + C. L