MAT 1322 Lecture Notes - Improper Integral, Antiderivative, Befehlshaber Der U-Boote

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1322
• Professor: Termeh Kousha

Document Summary

1. 2 finding the area between two curves . Suppose that f (x) and f (x) are functions such that f (cid:48)(x) = f (x) then we say that f (x) is an antiderivative of f (x). (cid:90) 1. 1 common inde nite integrals: for any constant k,(cid:90) (cid:90, for any real number n except -1, k dx = kx + c. 1 n + 1 xn+1 + c. (cid:90) 1 (cid:90) x dx = ln|x| + c. ex dx = ex + c. 1. 1. 1 rules for integrals: for any constant k and function f (x), (cid:90) (cid:90) kf (x) dx = k f (x) dx. (cid:90) (cid:90) (cid:90, for any functions f (x) and g(x), (f (x) + g(x)) dx = Ex: find each of the following inde nite integral : (cid:82) 5ex 3x 2+ f (x) dx + g(x) dx. Ex: given that f(cid:48)(x) = e3x + 4 and f (0) = 2, nd the function f (x).