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!
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!!!
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
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.
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.