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STANDARD 3.4D2

Volumes of solids with known cross sections, including discs and washers, can be calculated with definite integrals.

WORKSHEETS

Practice-Using Definite Integrals to Calculate Volume 1a
MC,
disc, x-axis, polynomial, rational, radical, trigonometric

8 PDF

Practice-Using Definite Integrals to Calculate Volume 1b
open ended,
disc, x-axis, polynomial, rational, radical, trigonometric

10 PDF

Practice-Using Definite Integrals to Calculate Volume 2a
MC,
disc, y-axis, polynomial, rational, radical, trigonometric

8 PDF

Practice-Using Definite Integrals to Calculate Volume 2b
open ended,
disc, y-axis, polynomial, rational, radical, trigonometric

10 PDF
Practice-Using Definite Integrals to Calculate Volume 3a
MC,
disc, shifted from axis, polynomial, radical
8 PDF
Practice-Using Definite Integrals to Calculate Volume 3b
open ended,
disc, shifted from axis, polynomial, radical
10 PDF
Practice-Using Definite Integrals to Calculate Volume 4a
MC, disc, algebraic manipulation, polynomial, radical
8 PDF
Practice-Using Definite Integrals to Calculate Volume 4b
open ended, disc, algebraic manipulation, polynomial, radical
10 PDF
Practice-Using Definite Integrals to Calculate Volume 5a
MC, washer
, x-axis, polynomial, rational, radical, trigonometric
8 PDF
Practice-Using Definite Integrals to Calculate Volume 5b
open ended, washer
, x-axis, polynomial, rational, radical, trigonometric
10 PDF
Practice-Using Definite Integrals to Calculate Volume 6a
MC, washer
, y-axis, polynomial, rational, radical, trigonometric
8 PDF
Practice-Using Definite Integrals to Calculate Volume 6b
open ended, washer
, y-axis, polynomial, rational, radical, trigonometric
10 PDF
Practice-Using Definite Integrals to Calculate Volume 7a
MC, washer
, shifted from axis, polynomial, radical
6 PDF
Practice-Using Definite Integrals to Calculate Volume 7b
open ended, washer
, shifted from axis, polynomial, radical
12 PDF
Practice-Using Definite Integrals to Calculate Volume 8a
MC, washer, algebraic manipulation, polynomial, radical
8 PDF
Practice-Using Definite Integrals to Calculate Volume 8b
open ended, washer, algebraic manipulation, polynomial, radical
10 PDF
Practice-Using Definite Integrals to Calculate Volume 9a
MC, x-axis, square, rectangle, semicircle cross sections
12 PDF
Practice-Using Definite Integrals to Calculate Volume 9b
open ended, x-axis, square, rectangle, semicircle cross sections
12 PDF
Practice-Using Definite Integrals to Calculate Volume 10a
MC, x-axis, triangle cross sections
12 PDF
Practice-Using Definite Integrals to Calculate Volume 10b
open ended, x-axis, triangle cross sections
12 PDF
Practice-Using Definite Integrals to Calculate Volume 11a
MC, y-axis, square, rectangle, semicircle, triangle cross sections
12 PDF
Practice-Using Definite Integrals to Calculate Volume 11b
open ended, y-axis, square, rectangle, semicircle, triangle cross sections
12 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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