BIOL 1111 Lecture 1: LawsOfIndefiniteAndDefiniteIntegrals

• School: University of Windsor
• Department: Biological Sciences
• Course: BIOL 1111
• Professor: Animesh Sarker

Document Summary

Laws/theorems/de nitions required for inde nite and de nite integrals: de nition: a function f is called an antiderivative of f on an interval. I if f (x) = f (x) for all x in i: theorem: if f is an antiderivative of f on an interval i, then the most general antiderivative of f on i is. F (x) + c where c is an arbitrary constant: basic forms xn+1 n + 1. 1 + x2 dx = tan 1 x + c dx = sin 1(cid:16) x (q) z. 1 a a(cid:17) + c a(cid:17) + c a(cid:17) + c. We let x0(= a), x1, x2, , xn(= b) be the endpoints of these subintervals and we let x n be any sample points in these subintervals, so x i lies in the ith subinterval [xi 1, xi]. Then the de nite integral of f from a to b is.