 y’ = 3x and y’ = x are examples of differential equations  Differential Form dy = f(x) dx

 Is the operation of finding all solutions of this equation and is denoted by an integral sign ∫  General Solution › y = ∫ f(x) dx = F(x) + C * Integration is the “inverse” of differentiation

 Describe the antiderivative of 3x

 Many applications of integration you will be given enough information to determine a particular solution.  Need the initial condition, the value of y =F(x) for one value of x

 Use initial condition F(1) = 0

 F(1) = -1 + C = 0

 Online book lesson 4.1 Exercises  3-42 multiples of 3 and 55-62

 A ball is thrown upward with an initial velocity of 64 feet per second from an initial height of 80 feet. › Find the position function giving the height s as a function of time t › When does the ball hit the ground?