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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

15.04

Double Integrals in Polar Coordinates

For disks, rings and sectors, switch to polar coordinates: dA becomes r dr dθ.

About 15 minutes

You'll learn to

→Convert double integrals to polar coordinates
→Explain the extra factor of r
→Integrate over disks, annuli and sectors
→Evaluate the Gaussian integral

← 15.03 Double Integrals over General Regions 15.05 Surface Area →

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