Average value and weighted average.

Description
Riemann definition of integration as an avegage value of the given function at various points including the starting and the end points is derived. The average height of a point on a semicircle is calculated with respect to x and then w. r.t the arc length. This video also gives the idea of weighted average and the witche's cauldron.
Prof. Haynes Miller, Maths,18.01 Single Variable Calculus, Fall 2006: 21. Work, Probability, Massachusetts Institute of Technology: MIT OpenCourseWare),http://ocw.mit.edu (Accessed July,11,2011). License: Creative Commons BY-NC-SA:http://ocw.mit.edu/terms/#cc