MATH 1ZA3 Study Guide - Quiz Guide: Riemann Sum

• School: McMaster University
• Department: Mathematics
• Course: MATH 1ZA3
• Professor: Chris Mc Lean

Document Summary

Basically, it"s the area under the curve of a graph, defined by the slope of the graph, the x-axis, and wherever you want the area to start/stop. In the diagram, 1 is an integral, from some point x1 to x2. However, since it is below the x-axis, it will have a negative value. But, when you have a curved graph, finding the area under it becomes a lot more difficult. That is why the area under a curve is typically approximated via a series of rectangles of infinitely thin width. The sum of these areas is called the riemann sum. The derivative, therefore, is the limit as riemann sums, centered at any point xi each rectangle approaches zero. Note: if your rectangles are centred at their midpoints, (cid:1876) =(cid:2869)(cid:2870)(cid:4666)(cid:1876) (cid:2869)+(cid:1876)(cid:4667) This is what connects derivatives to integrals, via what is called antiderivatives. Part 1: if f is continuous on [a,b], then (cid:1858)(cid:4666)(cid:4667)