Calculus 1 Lecture 4.2: Integration by Substitution

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[@darthboganis1356]

Using Integration by Substitution Methodology w/examples 8:00 Two Substitutions in One 1:08:30 Difficulty finding u: Trial and Error (1:19:42) - Algebraic manipulation to get a dx = du/? which cancels out the remaining x terms in the function .. because we only want terms involving u. Substitution involving a trig function 1:25:00 recognise that this will not work the way it is currently written. Take advantage of known trig identities within each component of the major function. The focus is still getting rid of all the x terms.

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Professor Leonard is teaching at a college, he just uploads videos of his lectures. The reason it is easier to find great online lectures is due to KZbin being a meritocracy, and usually the better videos get more views, in tern making them easier to find.

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I've listened to a lot of Prof. Leonard's videos, and here's what I've gathered. It seems he's had his fair share of bad teachers when he was coming up, and may even have had some classes that he really struggled with. But he persevered, finally learned the material in a way that made sense, and got a masters in math. He also seems to be a very empathetic guy who cares about his students. So he has devoted a lot of effort to figuring out how to explain what he eventually learned in a way that most people (with the sufficient prerequisite background) can understand. And even then, he realizes that we are sometimes rusty on those prerequisites, so part of his instructional approach is to patiently remind us of what we need to know to get the new stuff.

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+AliAA I have already finished Calculus 1-3 a few years ago, but I still re-watch these videos just to refresh my memory of various topics, lol. I crammed his Calculus 3 playlist a while ago as a preparation for Mathematical Physics, which at least here in Sweden is a lot about vector calculus, partial differential equations and Fourier/Laplace Transforms.

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@Wesley Richardson You still have notes from 7 years ago?

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Professor L, you've helped me immensely by providing a second lecture to run parallel to my class to see what I miss. Thank you so very much for all the effort. You've helped me come from a low C at the start to scoring the top A on test 3. You're the man. You embody what it means to teach. A grateful student

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[@edwinhenrich8555]

My uni lecturer: Today we're doing integration by substitution 5min later: Here's the fundamental theorem of calculus. And one more equation origin story you need to know... Test: Just integ by substitution

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[@nilamilo4348]

Thank you so much for uploading this. Substitution is one of the three concepts or applications I couldn't grasp for my calc one final coming up this week, and you showing all the steps in detail really helped me. My teacher and the book skip steps all the time and don't give any tips on assigning 'u'. You have restored my faith that I will pass the class. I can't thank you enough.

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literately i wasn't understand the integ. substitution and now i understood it how to solve it . thank u very much really

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*TIP:* By the time you finish his courses on Calc 1/2/3, if you're not already an "A+" student in Algebra, you WILL be. It's astonishing just how good you become at algebra when you're crunching derivatives and integrals every day and moving numbers around in the equations (something that used to give me problems). It becomes so easy that you won't even have to think about it any more. :)

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They don't dislike the video, they dislike the subject :)

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got taught this and came across problems like the ones you teach after 1:08 and thank you so much for making me understand, honestly ur a great teacher , wishhhhh i had you u rlly know what ur doing and ur not boring XD

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I always stop the lectures after you write down a problem to attempt it first. I did the one at 51:39, then took a break. When I came back and resumed to see the solution, I almost bought what you did at first thinking I overlooked a simple cancellation after having just spent 10 minutes solving it 🤣

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Many such cases

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[@salmanzaidi827]

For the example involving sec^2(piex), isnt that equivalent to (secpiex)^2, therefore the inside function would be secpiex Rather than piex

[@mrzeolite]

One thing to note for some (overly critical) professors, is that when canceling x, the variable cannot be in the denominator because it can be zero (see 1:03:00). I missed several homework points because of that, even though I ultimately ended with the correct solution each time....

[@johnkiserliss123]

Try using another variable ( not U ) as T is better.Because in integration by parts we use U & V & If you use U again in your substitution one might get confused which U is U.

[@ahmedfaris26]

That's a great idea!

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Prof Leonard makes math fun!