CAS MA 123 Lecture Notes - Lecture 34: Antiderivative

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 123
• Professor: John Bergdall

Document Summary

Ma123 lecture 34 fundamental theorem of calculus. Let f(x) be a continuous function on [a,b] If f(x) = and differentiable on (a,b) and f"(x) = f(x)! If g(x) is any antiderivative of f(x) on [a,b] >>> b x is the area function then f(x) is a continuous function [a,b] f (t ) dt. So if g = f * constant by mvt then g(a) = f(a) + c >>> g(a) = c because f(a) = 0 then g(b) = f(b) + g(a)! *** every continuous function has an antiderivative *** Example: e-x2 has no elementary antiderivative but it does have an antiderivative by i. x x e x2 dt is related to bell curve distbution x a. F (t ) dt a2 a1 f (t) dt. = constant d dx b x f (t ) dt) d dx x b f (t ) dt) d dx x b f (t ) dt)