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Chapter 15Multiple Integrals

0115.01Double Integrals over Rectangular Regions
0215.02Fubini's Theorem
0315.03Double Integrals over General Regions
0415.04Double Integrals in Polar Coordinates
0515.05Surface Area
0615.06Applications of Double Integrals
0715.07Triple Integrals
0815.08Triple Integrals in Cylindrical Coordinates
0915.09Triple Integrals in Spherical Coordinates
1015.10Jacobian Matrices
1115.11Variable Substitution with Multiple Integrals
1215.12Applications of Triple Integrals

Chapter 15 · Multiple Integrals

0115.01Double Integrals over Rectangular Regions
0215.02Fubini's Theorem
0315.03Double Integrals over General Regions
0415.04Double Integrals in Polar Coordinates
0515.05Surface Area
0615.06Applications of Double Integrals
0715.07Triple Integrals
0815.08Triple Integrals in Cylindrical Coordinates
0915.09Triple Integrals in Spherical Coordinates
1015.10Jacobian Matrices
1115.11Variable Substitution with Multiple Integrals
1215.12Applications of Triple Integrals

Topics / 15 Multiple Integrals

15.11

Variable Substitution with Multiple Integrals

Substitute new variables to simplify the region or the integrand, and multiply by |Jacobian|.

About 15 minutes

You'll learn to

→Apply the change of variables formula
→Choose substitutions that turn regions into rectangles
→Find areas of ellipses and other regions

← 15.10 Jacobian Matrices 15.12 Applications of Triple Integrals →

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