1 Antiderivative An antiderivative of a function f is a function F such that Ex.An antiderivative of since is Lecture 17 The Indefinite Integral Waner Section 6.1 Page 352~363

2 Which means: find the set of all antiderivatives of f. When you see this: Think this: “the indefinite integral of f with respect to x,” Integral sign Integrand Indefinite Integral x is called the variable of integration

3 Every antiderivative of a function must be of the form F(x) = G(x) + C, where C is a constant. Notice Constant of Integration Represents every possible antiderivative of 6x.

4 Power Rule for the Indefinite Integral Ex.

5 Indefinite Integral of x -1 Indefinite Integral of e x and b x

6 Sum and Difference Rules Ex. Constant Multiple Rule Ex.

7 Indefinite Integral Practice

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10 Indefinite Integral Practice

11 Indefinite Integral Practice

12 Integral Example (Different Variable) Ex. Find the indefinite integral:

13 Finding Cost from Marginal Cost Waner pg. 359 The marginal cost to manufacture baseball caps at a production level of x caps is 3.20 – 0.001x dollars per cap, and the cost of producing 50 caps is $200. Find the cost function.

14 Position, Velocity, and Acceleration Derivative Form If s = s(t) is the position function of an object at time t, then Velocity = v =Acceleration = a = Integral Form

15 Position, Velocity, and Acceleration Waner pg. 360 You toss a stone upward at a speed of 30 feet per second. a.Find the stone’s velocity as a function of time. How fast and in what direction is it going after 5 seconds? b.Find the position of the stone as a function of time. Where will it be after 5 seconds? c.When and where will the stone reach its zenith, its highest point?