Formula Sheet
                      Parametric Equations:
                                                        x=f(t),      y = g(t),  α≤t≤β
                      Slope of a tangent line:
                                                                 dy    dy     g′(t)
                                                                    = dt =
                                                                 dx    dx    f′(t)
                                                                        dt
                      Area:
                                                                  Z β g(t)f′(t)dt
                                                                   α
                      Arclength:
                                                            Z β p ′      2     ′    2
                                                                   (f (t)) +(g (t)) dt
                                                              α
                      Surface area:
                                                         Z β        p ′      2     ′   2
                                                             2πg(t)   (f (t)) +(g (t)) dt
                                                          α
                      Polar Equations:
                                                              r = f(θ),   α≤θ≤β
                      Polar coordinates to cartesian:
                                                           x=rcos(θ),        y = rsin(θ)
                      Cartesian coordinates to polar:
                                                            p 2      2                 y
                                                       r =    x +y ,        θ = arctan x
                      Slope of a tangent line:
                                                       dy    dy    f′(θ)sin(θ) +f(θ)cos(θ)
                                                          = dθ =
                                                      dx     dx    f′(θ)cos(θ)−f(θ)sin(θ)
                                                             dθ
                      Area:
                                                                  Z β 1       2
                                                                      2(f(θ)) dθ
                                                                   α
                      Arclength:
                                                            Z β p ′      2          2
                                                                  (f (θ)) +(f(θ)) dθ
                                                             α