MA 141 Study Guide - Final Guide: Antiderivative, Even And Odd Functions, Sine Wave
Document Summary
Just like with derivatives, once we have a formal de nition of a de nite integral, we can develop tools that let us compute the de nite integral in a faster or easier manner. Fundamental theorem of calculus: let f be continuous on [a, b]. A(x) = z x for all x [a, b] is an antiderivative of f on [a, b]. Part 2: if f is any antiderivative of f on [a, b], then a f (t)dt. Z b a f (x)dx = f (b) f (a). Part 2 is fundamental to our computation of de nite integrals as we develop more tools. Z b a f (x)dx = f (x)(cid:12)(cid:12)(cid:12) b a. First, part 1 says that the de nite integral of f from a to some endpoint x, or the area under the curve on [a, x] as x varies, can be calculated using an antiderivative of f .
