Triple Integrals in Spherical Coordinates
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- Опубліковано 7 сер 2024
- 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)
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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!
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
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!!!
This is outstanding to hear! Best of luck with EM theory! \o/
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.
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
prepping for calc 3 final, huge help
I really like the progression of the lesson. Very helpful!
Glad to hear that!
Thanks, very clear explanations and good exemples.
Luckily I found your video before the exam... I totally can't understand what's Rho and everything before watching your video... thanks!!!
You got this!
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)?
Remember that phi is measured from the positive axis downward. So if phi is from 0 to pi, that will give us a slice that is a semicircle in shape (in the xz-plane). If we take that semicircle and revolve it about the z-axis (which is the theta from 0 to 2pi part), we get the entire sphere.
If we used phi from 0 to 2pi, our slice would be an entire circle. This means we have two of the slices mentioned above both revolving about the z-axis to generate a sphere, and each of those slices would generate a sphere by itself which would give us double the sphere we want.
@@HoustonMathPrep thank you so much!
These videos reaaally help 😁✨
Thank you very much, sir. Awesome video.
You are welcome! Thank you for your kind words.
Its amazing ❤️
A lot of thanks ❤
Thanks man! It helped me a lot!
Glad to hear it!
This is amazing!!, thanks alot.
You're very welcome!
You saved my day ❤❤ semester credits goes to you☝
The credit is all yours! We just provided a little help 😁
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.
well done :)
Thnx 🙏
Welcome 😊