Match curve styles

styles = Sequence@@{ImageSize -> 400, Filling -> Axis, FillingStyle -> Opacity[0.1], PlotRange -> {0.01, All}, AxesOrigin -> {-0.01, 0.01}, PlotStyle -> (Directive[AbsoluteThickness[5], #]& /@ ColorData[68, "ColorList"])};

Plot[Table[Sqrt[Cos[t]] Exp[-x Sin[t] ^ 4], {x, {1, 10, 100, 1000, 10000}}]//Evaluate, {t, 0, Pi / 2}, Evaluate@styles, PlotLegends -> LineLegend[{1, 10, 100, 1000, 10000}, LegendMarkerSize -> {30, 10}, LegendLabel -> x, LabelStyle -> {GrayLevel[0.3], Bold, 16}]]

-Graphics-