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Chapter 16Line and Surface Integrals

0116.01Vector Fields
0216.02Line Integrals
0316.03Line Integrals of Vector Fields
0416.04The Fundamental Theorem for Line Integrals
0516.05Conservative Vector Fields
0616.06Green's Theorem
0716.07Area of Parametric Surfaces
0816.08Surface Integrals
0916.09Surface Integrals of Vector Fields
1016.10Stokes' Theorem
1116.11The Divergence Theorem
1216.12Applications of Line and Surface Integrals

Chapter 16 · Line and Surface Integrals

0116.01Vector Fields
0216.02Line Integrals
0316.03Line Integrals of Vector Fields
0416.04The Fundamental Theorem for Line Integrals
0516.05Conservative Vector Fields
0616.06Green's Theorem
0716.07Area of Parametric Surfaces
0816.08Surface Integrals
0916.09Surface Integrals of Vector Fields
1016.10Stokes' Theorem
1116.11The Divergence Theorem
1216.12Applications of Line and Surface Integrals

Topics / 16 Line and Surface Integrals

16.07

Area of Parametric Surfaces

Describe a surface with two parameters, r(u, v). The cross product r_u × r_v gives both a normal vector and the area scale.

About 15 minutes

You'll learn to

→Parametrize planes, spheres, cylinders and cones
→Find normal vectors with r_u × r_v
→Compute surface area as ∬|r_u × r_v| dA

← 16.06 Green's Theorem 16.08 Surface Integrals →

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