MATH 1010U Lecture Notes - Lecture 36: Symmetric Function, Riemann Sum
Document Summary
You may need to split 1 fraction into 2. Rewriting 1 such that it fits the du form. Even -> just integrate half of it (the other half is the same) **if boundary is [-a,a] check for this rule. Riemann sum: lim (to infinity) sum of i=1 to i=n y dx = y dx [1,0] A = (imagine it as taking a riemann sum of limited area: sum all the rectangles in that area, and take limit to get exact" value) Lim (to infinity) sum of i=1 to i=n (y 2 -y 1 ) dx = (y 2 -y 1 ) dx [a,b] For curve in general: a = (y 1 -y 2 ) dx [a,b] *set the boundaries to where the two curves intersect (equate the functions f(x)=g(x)) Imagine dividing the exact"(limit) of sum of rectangles = f(x) dx [a,b] Mvt for integrals f(x) must be continuous on interval [a,b]
