Uploaded February 2023 | Updated September 2026, 2 hours ago
Assignment 7, part 2.
In this video we calculate triple integrals over non-rectangular prisms (variable bounds). Sometimes we can take advantage of the product of single variable functions, sometimes we can't! These are not harder than double integrals, they just have an extra step! We need to work out the order of integration by looking at what bounds depend on what variables. If someone depends on x it goes before dx. If something depends on x and y, it goes before dx and dy, etc. The final problem is a triple integral over a tetrahedron where we need to write the equation of a plane!
(I often accidentally call these volumes, which they could sort of be...but not geometric volumes, more like the volume of a gas in the region described!)
These are fully worked out problems with commentary.
Time stamps:
0:00 Number 9
3:16 Number 11
6:17 Number 16
This is a common topic in Calculus III, Multivariable Calculus
Assignment 7, part 2.
In this video we calculate triple integrals over non-rectangular prisms (variable bounds). Sometimes we can take advantage of the product of single variable functions, sometimes we can't! These are not harder than double integrals, they just have an extra step! We need to work out the order of integration by looking at what bounds depend on what variables. If someone depends on x it goes before dx. If something depends on x and y, it goes before dx and dy, etc. The final problem is a triple integral over a tetrahedron where we need to write the equation of a plane!
(I often accidentally call these volumes, which they could sort of be...but not geometric volumes, more like the volume of a gas in the region described!)
These are fully worked out problems with commentary.
Time stamps:
0:00 Number 9
3:16 Number 11
6:17 Number 16
This is a common topic in Calculus III, Multivariable Calculus
