CAS MA 123 Lecture Notes - Lecture 30: Antiderivative
12 Nov 2015
School
Department
Course
Professor
Document Summary
Ma123 lecture 30 integrals continued and differential equations. Sec2( x) dx = tan(x) + c. Sec2(2x ) dx = tan(2x) + c. Lnx dx = x lnx - x + c. Possible to not be able to explicitly compute antiderivatives. Sec( ax) tan(ax) dx= 1 a sec (ax)+c. Setup: given a function g(x) and solve for f(x) (f"(x) = g(x)[differential equation] and f(a) = b[initial condition]) 1/3 (3)3 -2(3) + c ;solve for c and get 4. Conclude that f(x) = 1/3 x3 -2x + 4 unique function set. Start with an object moving with constant acceleration a, initial velocity vo, initial position so. Want to write s(t) = equation describing the motion. 2- differential equation problem {s"(t )=v (t ) 1- first problem to solve is {v" (t)=a v (0)=v0 s (0)=s0. Suppose acceleration @ time t is given by. The velocity function v(t) satisfies {v"(t )= 1.
