Khan Academy: Calculus: Parametrization of a Reverse Path

Video shows how to find the velocity and acceleration vectors of a particle at a given time by using the derivatives of the parametric equations representing the particle. Also shows how to find the magnitude of the velocity vector in...

This video [4:48] shows how to determine the integral of an unusual function using geometry to find the area under the curve. Also shows how to find the derivative of a function which contains an integral by using the Fundamental Theorem...

Video lesson explaining why the antiderivative is the area under a curve. Provides an introduction to the fundamental theorem of calculus. [9:46]

Video shows how to find the slope of the tangent line to a particles path using the derivatives of the parametric equations representing the particle. Also shows how to integrate the derivatives of the parametric equations along with...

Video lesson using line integrals to find the area along a parametric curve in both directions. Shows that the results are the same for either direction by using substitution. [16:22]

Part 1 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The first video sets up the surface integral for the entire surface, evaluates the first surface and parametrizes and finds the...

Part 3 of a 4-part video series solving for the surface integral of a surface made of three separate parts. The third video parametrizes the third surface, finds the magnitude of the cross product and begins to evaluate the double...

Part 1 of a 3-part video series showing how to calculate the surface integral of a torus. Video first reviews the parametrization of the torus and then starts to use it to find the surface area of the torus by finding partial...

Video lesson introducing conservative vector fields and the multivariable chain rule. Shows that a vector field is conservative if the line integral is the same for the same starting and ending point regardless of the path taken. [17:14]

Video lesson using line integrals in a vector field for a path in opposite directions. Gives the intuition and then shows that the results will have opposite signs. [15:51]