Triple Integrals in Spherical Coordinates

Calculus 3 tutorial video that explains triple integrals in spherical coordinates: how to read spherical coordinates, some conversions from rectangular/polar to spherical, what the integrals mean in terms of volume and mass using a density function, how to set them up, how to find the bounds for integration, and works through examples. Examples that you might see from a typical Calculus 3 course include: mass of a sphere with a given density function, volume inside both a cone and a sphere, and volume inside a cone and below a horizontal plane.
0:00 Introduction to spherical coordinates
4:05 Unit of volume in spherical coordinates
7:03 Example 1 (Mass of a sphere)
14:12 Example 2 (Volume inside cone & sphere)
19:26 Example 3 (Volume inside cone & below plane)

[soccerboss]

Finally a spherical integral video that actually explains the boundaries. Integrating should be the thing that comes easily but the bounds have been tripping me up. Thank you sir I probably won’t do well on my test tomorrow but I’ll definitely do bettter now thanks!

[joaquinmattecamus]

Absolute goat, as the level In calculus increases, the harder it is to find videos and this one explained how to find the boundaries perfectly

[seniorshimhanda]

This video incredibly enabled me to understand parametrization, a crucial step towards comprehending the electromagnetic theory. Now I can compute electric fields, electric potential and electrostatic energy with ease. HMP is basically the best math tutor online. Thank you for helping me overcome this hurdle: electromagnetism is the basis of my career!!!

[syahfA]

Finally I know why I need to learn this thing. Before this, I just calculate it without knowing the purpose. Thank youu sir. Good and clear explanation.

[の雪-mf]

Luckily I found your video before the exam... I totally can't understand what's Rho and everything before watching your video... thanks!!!

[mukhtarabdi]

Thank you so much. I go to through all your videos about double and triple integrals I really appreciate the simple and understandable way that you explained. Thanks again

[isisyasmim]

I really like the progression of the lesson. Very helpful!

[jordanfreidel]

Just one question, when setting the integral limits for dfi why do you only go half way around(pi) the sphere and not all the way around(2pi)?

[aSoulJourner]

Thanks, very clear explanations and good exemples.

[harshanasenevirathna]

You saved my day ❤❤ semester credits goes to you☝

[aarthiarulabi]

Thank you very much, sir. Awesome video.

[krishanbhalsod]

Question, when you were setting the triple integral for the last problem, why couldn't we solve for p and make that the upper bound, when we were given z=3 and phi=pi/3? Might be a dumb question.