Question

if f(x)= x in 0<x<2π then the value of bn is
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Answer 1

Step-by-step explanation:

(i)

2

2

c l

c

dx l

+

= ∫

(ii)

2 2

cos sin 0

c l c l

c c

m x m x dx dx

l l

p p

+ +

= = ∫ ∫

(iii)

2

cos sin 0

c l

c

m x n x dx

l l

p p

+

= ∫

for all integers m and n

(iv)

2 2

cos cos sin sin 0

c l c l

c c

m x n x m x n x dx dx

l l l l

p p p p

+ +

= = ∫ ∫

(for all integers m and n such that m≠ n)

(v)

2 2

2 2

cos sin

c l c l

c c

m x m x dx l dx