# Plotting a sum for a series of sine and cosine all within the same height on the x-y axis? [closed]

The limits of the graph should be (0,1) on the x and y axis but mine is [1,11] on x-axis and [0,7] on the y axis. Any idea what to do?

ListLinePlot[
Table[
2 π
(Sum[
2 E^(-n^2 π^2 t) π  *
NIntegrate[E^(-((1 - Cos[π y])/(2 π))) Cos[n π y], {y, 0,1}] *
n Sin[n π x],
{n, 1, 10}] /
(NIntegrate[E^(-((1 - Cos[π y])/(2 π))) , {y, 0, 1}] +
Sum[
2 NIntegrate[
E^(-((1 - Cos[π y])/(2 π))) Cos[n π y], {y, 0, 1}] *
E^(-n^2 π^2 t)* Cos[n π x],
{n, 1, 10}])),
{t, {0.3, 0.1, 0.05, 0.01, 0}},
{x, {0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1}}]]


That is because the table you made does not depend on x as

{{x ,f[x, t]},...}.


It is like

{ {f [xi , t1 ], ...} , { f [ xi , t2 ] , ...} , ... , { f [ xi , t5 ] , ... }  }.


so list line plot take the position number of the function's value in the list to be its x axis. That is why it starts from 1 and goes to 11 on X axis. So modify as follows:

ListLinePlot[
Table[{x,
2 \[Pi] (Sum[
2 E^(-n^2 \[Pi]^2 t) \[Pi]*
NIntegrate[
E^(-((1 - Cos[\[Pi] y])/(2 \[Pi]))) Cos[n \[Pi] y], {y, 0,
1}]*n Sin[n \[Pi] x], {n, 1,
10}]/(NIntegrate[
E^(-((1 - Cos[\[Pi] y])/(2 \[Pi]))), {y, 0, 1}] +
Sum[2 NIntegrate[
E^(-((1 - Cos[\[Pi] y])/(2 \[Pi]))) Cos[n \[Pi] y], {y, 0,
1}]*E^(-n^2 \[Pi]^2 t)*Cos[n \[Pi] x], {n, 1,
10}]))}, {t, {0.3, 0.1, 0.05, 0.01, 0}}, {x, 0, 1, .1}],
PlotRange -> {{0, 1}, {0, 1}}]


you can change the option PlotRange of the plot from

PlotRange->{{0,1},{0,1}}


to

PlotRange->{{0,1},All}


or

PlotRange->All


to get