Riemann Sum: Left Sum: Integral Middle Sum: Right Sum: Double Integral Triple NA NA NA Integral then Inverse Inverse Function Theorem: NA NA NA Functions where Polar: Rectangular 2D: Where Proof: Rectangular 3D: Circle: C = πd = 2πr Arc Length NA Cylindrical: Proof: s(t) Spherical: Curvature NA (See Wikipedia : Curvature) for r() where f(t) = (x(t), y(t), z(t)) Circle: C = πd = 2πr Square: P = 4s Ellipse: Perimeter Rectangle: P = 2l + 2w Circle: C = 2πr NA NA NA Triangle : P = a + b + c Ellipse:
Integral Riemann Sum: Left Sum: Middle Sum: Right Sum: Double Integral Triple Integral NA NA NA Inverse Functions Inverse Function Theorem: where then NA NA NA Arc Length Proof: Polar: Where Circle: Proof: C = πd = 2πr Rectangular 2D: Rectangular 3D: Cylindrical: Spherical: s(t) NA Curvature for r() NA where f(t) = (x(t), y(t), z(t)) (See Wikipedia : Curvature) Perimeter Square: P = 4s Rectangle: P = 2l + 2w Triangle : P = a + b + c Circle: C = πd = 2πr Ellipse: Ellipse: Circle: C = 2πr NA NA NA
Harolds_Calculus_3_Cheat_Sheet_2017.docx