ParametricPlot[{t-Sin[t],1-Cos[t]},{t,0,4*Pi},AxesLabel->None, Ticks->None]

ParametricPlot[{t-3/4*Sin[t],1-3/4*Cos[t]},{t,0,4*Pi},AxesLabel->None, Ticks->None]

ParametricPlot[{t-5/4*Sin[t],1-5/4*Cos[t]},{t,0,4*Pi},AxesLabel->None, Ticks->None]

Integrate[Sqrt[2+t^2],{t,0,Pi/2}]

ParametricPlot3D[{t,t^2/Sqrt[2],t^3/3},{t,0,2},AxesLabel->{x,y,z},Mesh->None,Boxed->False]

ParametricPlot3D[{t,3*t^2/2,3*t^3/2},{t,0,2},AxesLabel->{x,y,z},Mesh->None,Boxed->False]

ParametricPlot3D[{t*Cos[t],t*Sin[t],t},{t,0,Pi/2},AxesLabel->{x,y,z},Mesh->None,Boxed->False]

ParametricPlot3D[{Cos[2*t]/4 ,Cos[t]^3,Sin[t]^3},{t,-Pi/2,Pi/2},AxesLabel->{x,y,z},Mesh->None,Boxed->False]

Integrate[(Sqrt[1+4*x^2]+3x^2)*Sqrt[1+4*x^2],{x,0,1}]

Integrate[x*Sqrt[4*x^4+5*x^2+1],{x,1,2}]

Integrate[Exp[2*t]/t*Sqrt[1+t^2],{t,1,E^2}]

Integrate[R^2*h*t*Sin[t]*Cos[t]*Sqrt[R^2+h^2*t^2],{t,0,2}]