4A: Triple Integrals

Captured On [2020-02-06 Thu 16:38] Source Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates | Part A: Triple Integrals | 4. Triple Integrals and Surface Integrals in 3-Space | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Triple integrals Figure 2: Example of triple integral Figure 3: Setting up interated integral for triple integral Figure 4: Find shadow in \(xy\text{-plane}\) Figure 5: Computing iterated integral Figure 6: Better use polar coordinates for triple coordinates...

Captured On [2020-02-06 Thu 17:02] Source Session 75: Applications and Examples | Part A: Triple Integrals | 4. Triple Integrals and Surface Integrals in 3-Space | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Mass on triple integral Figure 2: Average value on triple integral Figure 3: Center of mass on triple integral Figure 4: Moment of inertia on triple integral Figure 5: Moment of inertia about axis...

Captured On [2020-02-06 Thu 17:03] Source Session 76: Spherical Coordinates | Part A: Triple Integrals | 4. Triple Integrals and Surface Integrals in 3-Space | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Spherical coordinates Figure 2: On a sphere \(\rho = a\) Figure 3: Transform from cylindrical to spherical coordinates Figure 4: Transform from spherical to rectangular coordinates Figure 5: Examples of figures on spherical coordinates...

Captured On [2020-02-06 Thu 17:04] Source Session 77: Triple Integrals in Spherical Coordinates | Part A: Triple Integrals | 4. Triple Integrals and Surface Integrals in 3-Space | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Triple integral in spherical coordinates Figure 2: Surface area on sphere of radius \(a\) Figure 3: Surface element Figure 4: Volume element Figure 5: Example of volume of unit sphere above \(z = 1 / \sqrt{2}\)...

Captured On [2020-02-06 Thu 17:05] Source Session 78: Applications: Gravitational Attraction | Part A: Triple Integrals | 4. Triple Integrals and Surface Integrals in 3-Space | Multivariable Calculus | Mathematics | MIT OpenCourseWare 1 Chalkboard Figure 1: Graviational force exerted by \(\Delta M\) Figure 2: Gravitational force vector Figure 3: Setting up triple integral on an axis of symmetry Figure 4: Use spherical coordinates Figure 5: Newton’s Theorem Figure 6: Newston’s Theorem (II)