MATH 1P97 Lecture Notes - Lecture 11: Trapezoidal Rule, Riemann Sum, Farad

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P97
• Professor: Sandra Yee

Document Summary

Chapter 7. 3 f ( x) 0 on [a ,b] to simplify the derivation of the. The result is valid without this restriction. Begin by dividing the interval [a,b] into subintervals of equal length. By means of the (n+1) points x-0= a , x-1, x-2, x-n= b where n is a. Then the length of each subinterval is given by. X= b a n b a f ( x) dx. Furthermore as we saw earlier, we may view the definite integral as the area of the region r under the curve y=f (x) between x=a and x=b. This are is given by the sum of the areas of the n nonoverlapping subregions. R1,r2 where each rn represents the region under the curve y=f (x) A much better approximation than one obtained by means of rectangles (a. The region of rn is categorized by the following equation: ( f (xn)+f (xn +1)