One of Calculus's Most Famous Theorems Explained Visually
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- Опубликовано: 16 сен 2024
- #maths #apcalcab #science #apcalcprep #apcalculusbc #mathematics #integration #interesting #proof #visualization
Integration by Parts is one of calculus's most famous integration theorems. However, although the way it is usually proved as a result of the product rule of differentiation is effective, it lacks any visual intuition. This video aims to correct that by providing an interesting way of viewing integration by parts visually.
This video was based on a "Proof without Words" titled "Integration by Parts" by Richard Courant. This proof comes from Volume 1 of the book Proofs Without Words: Exercises in Visual Thinking by Roger B. Nelson.
Works Cited:
Nelsen, R. B. "Trigonometry, calculus, & analytic geometry." Proofs without words: Exercises in visual thinking, American Mathematical Soc., 2020, p. 42.
Hey all, this is my first video of this summer and I plan on posting a bit more frequently over the next few months. Be on the lookout for those videos in the future!
Fantastic video, simple and elegant, God Bless, Keep up the spirit, have a good time🎉
THIS VIDEO IS SO GOOOD MAAAN THXX KEEP UP THE GREAT QUALITY 🗣️🗣️
Un alt mod de abordare a demonstrării formulei integrării prin părți, extrem de elegant, distinct de ceea ce ătiam din școală. Foarte frumos. E o plăcere să urmărești așa ceva. Succes în continuare.
amazing work man. Keep it up.
It is a great video, but I did not understand that (1:36) why the length of the short side of the rectangle is dx or du?
The rectangle with width du is showing an arbitrary rectangle with a height of the function f(x) and an arbitrary width du such that when infinite rectangles of infinitesimal width are summed along the u axis, the area under the curve is produced. The same logic applies to the rectangle with width dv except that the axis being integrated along is the v axis. Essentially, the rectangles are showing the Riemann sums being performed along the horizontal and vertical axes to acquire the areas between the curve and the horizontal and vertical axes. Hope this helped.
I’m not sure what audience this is intended for so take my criticism with a grain of salt. I think that the video is fantastic, however, if the intended audience is those unfamiliar with integration by parts, I think there should be some audio explaining your logic as I can imagine this might be more difficult to follow for less experienced viewers. Keep up the good work!