Clip 1.  Areas - Integration with Care. 

    This example demonstrates the need to understand limits as well the geometry of problems when using calculus to compute exact areas. It uses the modulus function to re-establish the practical interpretation of a symbolic “negative area.”

V-Rec Static Transcripts

     The illustrations and hand-calculations presented in these 3 clips are available for download as a single static file that was edited for note-taking.

Clip 2.  A quick review of regular volumes of spheres, prisms and pyramids.

Clip 3.  Solids of Revolutions - exact volume calculations and the beauty of Calculus.