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Curriculum Guide

Advanced Placement Calculus Page 20

Antiderivatives

LO 3.1A

EK 3.1A1

EK 3.1A2

LO 3.3B(a)

EK 3.3B3

EK 3.3B5

Recognize antiderivatives of

basic functions.

An antiderivative of a

function f is a function

g whose derivative is f.

Differentiation rules

provide the foundation for

finding antiderivatives.

Calculate Antiderivatives

The notation ∫풇(풙)풅풙=

푭풙+푪 means that

푭′(풙)=풇(풙) and ∫풇(풙) is

called an indefinite integral

of the function f.

Techniques for finding

antiderivatives include

algebraic manipulation such

as long division and

completing

the square, substitution of

variables.

Indefinite Integral rules

Power rules

Trigonometric rules

Exponential and logarithmic

rules

Inverse trigonometric rules

Larson/Hostetler Calculus

8 th

4.1, 5.2, 5.3, 5.4, 5.5, 5.7

Ed.

25