f = 
      Sin[2 Pi x/L]*
        Cos[4 Pi x/L]

L = 1

Plot[f, {x, 0, 1}]

g2 = -(1/2) 
        Sin[2  Pi x/L]

g6 = (1/2) 
        Sin[6 Pi x/L]

g = g6 + g2

Plot[g2, {x, 0, 1}]

Plot[g6, {x, 0, 2}]

Plot[g, {x, 0, 1}]

w2 = c*2  Pi/L

tau2 = 2  Pi/w2

w6 = c*6 Pi/L

tau6 = 2 Pi/w6

c = 2

g2t = g2*Cos[w2 t]

g6t = g6*Cos[w6 t]

Do[Plot[{g2t}, {x, 0, 1}, PlotRange -> {- .5,  .5}], {t, 0, 
        tau2, 0.01}]

Do[
      Plot[{g6t}, {x, 0, 1}, PlotRange -> {- .5,  .5}], {t, 0, tau6, 
        0.005}]

Do[
      Plot[{g2t + g6t}, {x, 0, 1}, PlotRange -> {-1.5, 1.5}], {t, 0, 
        tau2, 0.01}]

Do[
      Plot[{g2t + g6t}, {t, 0, 2*tau2}], {x, 0, L, 0.1}]

f2 = x^2 - L*x

Plot[f2, {x, 0, 1}]

An = 
      Integrate[f2*Sin[n Pi x/L], {x, 0, L}]

An /. n -> 3

Plot[{f2, 
        Refine[Sum[(2/L)*An*Sin[(Pi/L) n x], {n, 1, 20}]]}, {x, 0, 
        1}]

Do[
      Plot[Sum[(2/L)*An*Sin[(Pi/L) n x]*Cos[(c*n Pi/L) t], {n, 
            1, 20}], {x, 0, 1}, PlotRange -> {- .3,  .3}], {t, 0, 1, 
        0.01}]

Cambiamos...

Cn = ((4 d Cos[((n π)/4)] Sin[((n π)/4)]^2)/(n π))

Plot[
      Refine[Sum[(2/d)*Cn*Sin[(Pi/d) n x], {n, 1, 15}], {d == 
            2}], {x, 0, 2}, PlotRange -> {-0.5, 1.5}]

A ver ....

Integrate[
      Sin[n Pi x/h], {x, h/4, 3 h/4}]