Here,f(x)=ex Also, (0,L)= (0,l) ⟹L=l a0=2L∫0Lfx dx a0=2l∫0l ex dx a0=2lex0l a0=2lel-e0 a0=2lel-1 πan=2L∫0Lfx cosnπxL dx ππan=2l∫0lex cos nπxl dx Here, a=1 ; b=nπl ππππan=2lex1+n2 π2l21cosnπl+nπlsinnπl0l ππππan=2ll2l2+n2 π2ex1cosnπl+nπlsinnπl0l πππππan=2ll2l2+n2 π2elcosnπ+nπlsinnπ-e0cos0+nπlsin0 πππan=2ll2+n2 π2el-1n+nπl0-e01+nπl0 πan=2ll2+n2 π2el-1n-1 Now, Fourier series of f(x) is, πf(x)=a02+∑n=1∞an cosnπxl ππ⇒f(x)=1lel-1+∑n=1∞2ll2+n2 π2el-1n-1cosnπxl