Integral of the Day: 1.31.23 | EXTRA SPICY Trig Sub | Calculus 2 | Math with Professor V

WARNING: This integral is extra spicy and not for the faint of heart! Nothing is too complex, but it is tedious and felt like an appropriate way to close out the month. Thank you all for your views, comments, and continued support. I so appreciate it. Keep 'em coming, and let me know how you enjoyed today's I.O.T.D. (Integral of the Day). :)

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Professor V

Calculus 2 Lecture Videos on Integration:

Trig Review:

Calculus 3 Video Lectures:

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[MikeMagTech]

Thank you. That was great! You have inspired me to go back and review trig...again! Speaking of which, it is interesting to see how trig has evolved. It started out as a way to understand the natural world, then became a tool for Greek, Roman, etc., engineers, who used it to spectacular effect. Then, it was used extensively in navigation, where the chord, which does not seem to be taught any longer, was an important element. Now we have come full circle and are using it for all of the above, but also in truly creative ways as you demonstrated above.
I love calculus. It is an amazingly versatile and useful tool. And, like truly great tool, it is beautiful not only for what it is, but also for what it allows you to do.

[georgesadler]

Professor V, thank you for a lengthy and challenging Integral of the day. I worked out this Integral and it takes about twenty minutes to arrive at the correct solution. Professor V, the solution you get matches my solution step by step. Calculus students worldwide should know and understand the Trigonometry that's involved in this Integral. This video/lecture contains no errors.

[d.h.y]

What a beautiful penmanship you have! Your students are blessed to take classes from a professor like you 😎😎