Integrals of trig functions and reduction formulae. Chris Tisdell UNSW Sydney

[Kurtlane]

Great lecture. Thanks.

But I find one place going too fast for me. It comes right after change of coordinates (Cartesian to polar) when calculating total mass of a quarter of a circle with uneven density (18:00 - 20:10).

I understand the change itself, but (around 19:30) the M= followed by 2 integrals, one inside the other, and then equal to 2 integrals multiplied by each other, and they seem to be partial integrals.

(cont.)

[Kurtlane]

But we haven't been introduced to partial integrals yet.

Am I right? Are integrals inside each other equal to products of partial integrals? Or is there something else going on?

[DrChrisTisdell]

@Kurtlane The part of the lecture to which you refer is an "enrichment" example as I would not expect the audience to have seen double integrals yet. However, roughly speaking you evaluate them by performing the inside integral first (holding other variables fixed) and then performing the outside integral. The answer will be a number (rather than, say, a function). Under certain circumstances a double integral is the product of two single integrals, but this is not true in general.

[Kurtlane]

@DrChrisTisdell, thanks. I get it.

[MsNANANA1234]

So much better than lecturer at usyd

[AdRenaLinMMIX]

Thanks for posting this. You've made things clear and easy to understand, it's just annoying how the writing is out of sync with your speech!

[richardcmul]

Thank you so much, Dr. Chris! I'm a retiree living in Bogota, Colombia who finally has time to brush up on what interests me most--mathematics.  I for one am delighted to find your classes available here on Youtube.

Rich Mullen

[DrChrisTisdell]

@richardcmul I'm currently posting an entire set of lectures (Calc 2) online with accompanying PDFs of the notes. Hopefully everything will be ready in the next week, so please check back and let me know what you think of the associated notes.

Best wishes, Chris.