Mathematics-I (3110014)

BE | Semester-1   Winter-2019 | 17-01-2020

Q3) (b)

Obtain the fourier cosine series of the function fx=ex.

Here,f(x)=ex

Also, (0,L)= (0,l)

L=l

a0=2L0Lfx dx

a0=2l0l ex dx

a0=2lex0l

a0=2lel-e0

a0=2lel-1

an=2L0Lfx cosnπxL dx

an=2l0lex cos nπxl dx                                                              Here, a=1  ;  b=l

an=2lex1+n2 π2l21cosl+lsinl0l

an=2ll2l2+n2 π2ex1cosl+lsinl0l

an=2ll2l2+n2 π2elcos+lsin-e0cos0+lsin0

an=2ll2+n2 π2el-1n+l0-e01+l0

an=2ll2+n2 π2el-1n-1

Now, Fourier series of f(x) is,

f(x)=a02+n=1an cosnπxl

f(x)=1lel-1+n=12ll2+n2 π2el-1n-1cosnπxl