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why is

the sine series for f(x) = { 0 x<2 on 0,3

2 x>2

L=3

cn=2/3 int b=3 and a =0 f(x) sin( nxpi/ L)dx

= 2/3 int. b=2 a=0 (0) sin( pi n x/ 3) dx + 2/3 int b=3 a =2 (2) sin n x pi/3 dx

= 0 + 4/3{-3n pi cos n pi x/3} x=3 and x=2 = 4/n pi { cos 2 n pi/3 - cos n pi }

f(x)=sigma n=1 4/n pi { cos 2n pi/3 -(-1)^n sin n pi x

cos 2 pi/3=-1/2....

f(x)=4/pi( 2/3 sin pix/3-3/4sin2 pi x/3 +2/3sin 3 pi x/3...

how did they get this? very confused

the sine series for f(x) = { 0 x<2 on 0,3

2 x>2

L=3

cn=2/3 int b=3 and a =0 f(x) sin( nxpi/ L)dx

= 2/3 int. b=2 a=0 (0) sin( pi n x/ 3) dx + 2/3 int b=3 a =2 (2) sin n x pi/3 dx

= 0 + 4/3{-3n pi cos n pi x/3} x=3 and x=2 = 4/n pi { cos 2 n pi/3 - cos n pi }

f(x)=sigma n=1 4/n pi { cos 2n pi/3 -(-1)^n sin n pi x

cos 2 pi/3=-1/2....

f(x)=4/pi( 2/3 sin pix/3-3/4sin2 pi x/3 +2/3sin 3 pi x/3...

how did they get this? very confused

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