Double Integrals in Polar Coordinates

Calculus 3 video that explains double integrals in polar coordinates. We talk about where the polar unit of area "r dr d theta" comes from, and how to find bounds for your integrals based on the region of integration. We work a few different examples, finding volumes of some solids using a double integral in polar coordinates. Includes typical examples seen in a Calculus 3 type course with volumes involving paraboloids and cones.
0:00 Introduction to the polar unit of area
5:16 Example 1
9:32 Example 2 (Volume below a paraboloid)
13:41 Example 3 (Volume between cone & plane)

[ocean]

This is so much better than the explanation given in the Thomas's calculus Book! Thank you. Appreciate your work so much!

[ericjamieson]

Fantastic walk-through and examples, using this with Paul's online notes makes the concept much more digestible. btw, the handwriting in the video feels reminiscent of khan academy vids which makes it that much better. Thanks for the help! :D

[halaanbar-koez]

Thank you so much, amazing explanation, you have a great talent for teaching .

[evanchartrand]

Excellent, Thanks for saving my butt from a sub-par prof

[Isaac.Garcia]

when you turn the x^2 +y^2 into r^2 don't you factor out a negative making it (4+r^2)?