The Indefinite Integral

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Presentation transcript:

The Indefinite Integral

Antiderivative An antiderivative of a function f is a function F such that Ex. An antiderivative of is since

Indefinite Integral The expression: read “the indefinite integral of f with respect to x,” means to find the set of all antiderivatives of f. x is called the variable of integration Integrand Integral sign

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

Power Rule for the Indefinite Integral, Part I Ex.

Power Rule for the Indefinite Integral, Part II Indefinite Integral of ex and bx

Sum and Difference Rules Ex. Constant Multiple Rule Ex.

Integral Example/Different Variable Ex. Find the indefinite integral: Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.

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

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.