antiD[t_]=Integrate[t^2 Sin[t],t]

antiD[0]

antiD[t]-antiD[0]+1/2

antiD1[t_]=Integrate[t E^(-t),t];
p[t_]=antiD1[t]-antiD1[0]+1;
antiD2[t_]=Integrate[p[t],t];
antiD2[t]-antiD2[0]-1

cyclopid=ParametricPlot[{t-Sin[t],1-Cos[t]},{t,0,4 Pi}]

ParametricPlot[{Cos[t](1-Cos[t]),Sin[t](1-Cos[t])},{t,0,2Pi}]

ParametricPlot[{Cos[t]^3,Sin[t]^3},{t,0,2Pi}]

ParametricPlot[{Cos[t]/(1+Sin[t]^2),Sin[t]Cos[t]/(1+Sin[t]^2)},{t,0,2Pi}]

PolarPlot[Log[t+1],{t,0,5Pi}]

PolarPlot[Sin[5 t],{t,0,Pi}]

PolarPlot[Sin[7 t],{t,0,Pi}]

ContourPlot[x^2+y^2==1/2,{x,-1,1},{y,-1,1}]

ContourPlot[Cos[x]+Cos[y]==1/2,{x,0,4Pi},{y,0,4Pi}]

ContourPlot[Cos[x]+Cos[y],{x,0,4Pi},{y,0,4Pi}]

Plot3D[Sqrt[1-x^2-y^2],{x,-1,1},{y,-1,1}]

p1=ParametricPlot3D[{Sin[u] Cos[v],Sin[u]Sin[v],Cos[u]}, {u,0,Pi},{v,0,2Pi}];
p2=ParametricPlot3D[{1/2Cos[v],1/2Sin[v]+1/2,u}, {u,-1,1},{v,0,2Pi}];
Show[p1,p2, PlotRange->{{-1,1},{-1,1},{-1,1}}]

p1=ParametricPlot3D[{u Cos[v],u Sin[v]+1/2,Sqrt[1-(u Cos[v])^2-(u Sin[v]+1/2)^2]}, {u,0,1/2},{v,0,2Pi}];
p2=ParametricPlot3D[{u Cos[v],u Sin[v]+1/2,-Sqrt[1-(u Cos[v])^2-(u Sin[v]+1/2)^2]}, {u,0,1/2},{v,0,2Pi}];
Show[p1,p2, PlotRange->{{-1,1},{0,1},{-1,1}}]