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STANDARD 3.3B5

Techniques for finding antiderivatives include algebraic manipulation such as long division and completing the square, substitution of variables, (BC) integration by parts, and nonrepeating linear partial fractions.

WORKSHEETS

Practice-Techniques for Finding Antiderivatives 1a
MC, with substitution of polynomial, polynomial, rational, radical

12 PDF

Practice-Techniques for Finding Antiderivatives 1b
open ended, with substitution of polynomial, polynomial, rational, radical

20 PDF
Practice-Techniques for Finding Antiderivatives 2a
MC, with substitution of logarithmic, polynomial, rational, radical
12 PDF
Practice-Techniques for Finding Antiderivatives 2b
open ended, with substitution of logarithmic, polynomial, rational, radical
20 PDF
Practice-Techniques for Finding Antiderivatives 3a
MC, with substitution of exponential, polynomial, rational, radical
12 PDF
Practice-Techniques for Finding Antiderivatives 3b
open ended, with substitution of exponential, polynomial, rational, radical
20 PDF
Practice-Techniques for Finding Antiderivatives 4a
MC, with substitution of trigonometric, polynomial, rational, radical
14 PDF
Practice-Techniques for Finding Antiderivatives 4b
open ended, with substitution of trigonometric, polynomial, rational, radical
20 PDF
Practice-Techniques for Finding Antiderivatives 5a
MC, with substitution of polynomial, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 5b
open ended, with substitution of polynomial, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 6a
MC, with substitution of logarithmic, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 6b
open ended, with substitution of logarithmic, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 7a
MC, with substitution of exponential, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 7b
open ended, with substitution of exponential, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 8a
MC, with substitution of trigonometric, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 8b
open ended, with substitution of trigonometric, logarithmic rule and exponentials
20 PDF
Practice-Techniques for Finding Antiderivatives 9a
MC, with substitution of polynomial,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 9b
open ended, with substitution of polynomial,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 10a
MC, with substitution of logarithmic,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 10b
open ended, with substitution of logarithmic,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 11a
MC, with substitution of exponential,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 11b
open ended, with substitution of exponential,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 12a
MC, with substitution of trigonometric,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 12b
open ended, with substitution of trigonometric,
trigonometric
20 PDF
Practice-Techniques for Finding Antiderivatives 13a
MC, with substitution of polynomial,
inverse trigonometric
16 PDF
Practice-Techniques for Finding Antiderivatives 13b
open ended, with substitution of polynomial,
inverse trigonometric
16 PDF
Practice-Techniques for Finding Antiderivatives 14a
MC, with substitution of logarithmic,
inverse trigonometric
16 PDF
Practice-Techniques for Finding Antiderivatives 14b
open ended, with substitution of logarithmic,
inverse trigonometric
16 PDF
Practice-Techniques for Finding Antiderivatives 15a
MC, with substitution of exponential,
inverse trigonometric
14 PDF
Practice-Techniques for Finding Antiderivatives 15b
open ended, with substitution of exponential,
inverse trigonometric
14 PDF
Practice-Techniques for Finding Antiderivatives 16a
MC, with substitution of
trigonometric, inverse trigonometric
14 PDF
Practice-Techniques for Finding Antiderivatives 16b
open ended, with substitution of
trigonometric, inverse trigonometric
14 PDF
Practice-Techniques for Finding Antiderivatives 17a
MC, definite integral with substitution of polynomial, polynomial, rational
20 PDF
Practice-Techniques for Finding Antiderivatives 17b
open ended, definite integral with substitution of polynomial, polynomial, rational
20 PDF

BC

Practice-Techniques for Finding Antiderivatives 18a
MC, integration by parts, basic
8 PDF
Practice-Techniques for Finding Antiderivatives 18b
open ended, integration by parts, basic
10 PDF
Practice-Techniques for Finding Antiderivatives 19a
MC, integration by parts, advanced
8 PDF
Practice-Techniques for Finding Antiderivatives 19b
open ended, integration by parts, advanced
10 PDF
Practice-Techniques for Finding Antiderivatives 20a
MC, integration by parts twice, basic
5 PDF
Practice-Techniques for Finding Antiderivatives 20b
open ended, integration by parts twice, basic
5 PDF
Practice-Techniques for Finding Antiderivatives 21a
MC, integration by parts twice, advanced
4 PDF
Practice-Techniques for Finding Antiderivatives 21b
open ended, integration by parts twice, advanced
7 PDF
 

To access Practice Worksheets aligned to the College Board's AP Calculus Curriculum Framework, click on the Essential Knowledge Standard below.  To see the text of an EKS, hover your pointer over the Standard.
LIMITS 1.1A1 1.1A2 1.1A3 1.1C2 1.1C3 1.2A2 1.2A3            
DERIVATIVES 2.1A1 2.1A2 2.1A3 2.1C1 2.1C2 2.1C3 2.1C4 2.1C5 2.1C6 2.1D1 2.2A1 2.2A2 2.2A3
2.3A2 2.3B1 2.3B2 2.3C1 2.3C2 2.3C3 2.3F1 2.4A1          
INTEGRALS 3.2A1 3.2B2 3.3B1 3.3B2 3.3B3 3.3B5 3.4B1 3.4C1 3.4D1 3.4D2 3.5A1 3.5A2 3.5A3
SERIES 4.1A2                        
COMPLETE JMAP FOR CALCULUS

 

 

 
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