U-Substitution Example 7 (KristaKingMath)

U-Substitution calculus example.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[NomadicWanderer]

Two math professors go into a bar, arguing about how much the average person knows about calculus. As one sits down at a table, the other goes to the bar and orders drinks from the bartender. She then says to the bartender, "When you bring the drinks over, I'll ask you a question, and whatever it is, you answer, "x to the fourth over four." Then she slips him a five. When she returns to the table, she says to her friend, "I think the average Joe knows more about calculus than you think. In fact, I will bet you ten dollars that if we ask the bartender the integral of x^3, he'll know the answer." "Hah, " says the friend. "You're on." When the bartender arrives at the table, the first professor says, "Excuse me, but can you answer a question for us? What's the integral of x^3?" The bartender answers, "That's easy, x to the fourth over four.... +C."

[MasterTenblades]

@ Ray Bob - "pervert" lol we are here for math! focus! 

[kristakingmath]

@sSstrawb3rryy I wish you could have found me earlier as well! Hopefully you'll have enough time to turn it around. I'm happy that I'm able to help. :)

[kristakingmath]

Oh no! Try to stay confident and not get too stressed out. I know it's really hard, but you can definitely get through this and get to uni to do computer science. :) You have to solve for dx so that you can substitute a value for dx that's in terms of du. The goal is to have no x's left at all after substitution (you need u and du instead of x and dx). And you're right about du/3, because that's the same as (1/3)du, and when you have a constant coefficient like 1/3, you can move it in front of

[kristakingmath]

In most cases, you would set u equal to everything under the square root sign. So in your example, u=2x^2+1. du=4xdx, so dx=du/4x. Once you make the substitution, you should be able to cancel the x. If you can't canel the 1/4, you can still bring it out in front of your integral so that you don't have to deal with it in the integration. Hope this helps! :)

[kristakingmath]

@fingerboy18 It's definitely not wrong. It doesn't matter what you've got with dx, you can divide du by all of it and make the substitution. You'd substitute du/(4x^3) for dx in your integral, then hopefully try to cancel out the x^3 with another term in your problem. Remember that you'll be able to pull out 1/4 as a constant outside of the integral as well, if you want to. :)

[kristakingmath]

unfortunately, there isn't a faster method for solving an integral like this. however, if you practice this method a lot, you won't need to write out all the steps and you'll get much faster. as far as books, i always suggest james stewart's calculus, 6th or 7th edition, if you can get it. :)

[kristakingmath]

I have lots of videos where I manipulate the u-sub, but I can't find them, which tells me I'm very bad at tagging my own videos! :) However, I'd recommend plugging your integral into wolframalpha(dot)com, and that'll give you the step-by-step solution and the answer!! :D

[kristakingmath]

I can't imagine a professor who would call the square root correct, but not give you points if you wrote it as ^1/2. They're exactly the same so either should work. That being said, my personal preference is to put things back in terms of the square root in my final answer. :)

[kristakingmath]

you might be able to use trigonometric substitution. you can search for that in youtube and you'll find videos of mine, and others, that will show you how to use it. :)

[kristakingmath]

You're welcome! I have some trig integrals here: Hopefully they are helpful.

[kristakingmath]

@lmfao990 Yay! I'm happy you don't skip them anymore. :) Thanks for watching, I'm glad the videos are helping! :)

[buttronprime]

i love this teacher,  she is very clear in her explanations and has a lovely air. je t'aime!

[kristakingmath]

Wow awesome!!! All the way from Pakistan, that is so cool! Thanks for watching!! :D

[kristakingmath]

Wow awesome!!! All the way from Pakistan, that is so cool! Thanks for watching!! :D

[GreenCapElf]

It's 11:40 pm where I live and I've had horrible internet connection all day while searching for integral videos. The internet just came in and I decided to give it a shot and try to watch one final u-substitution video. IM GLAD I FOUND YOUR VIDEOS!! I finally understood U-subsitution thanks to you!

[kristakingmath]

I was always frustrated when teachers did that, so I do my best not to.

[kristakingmath]

Awww! You're so sweet! That makes me happy. :D

[kristakingmath]

@n1k00las You're very welcome! GOOD LUCK to you on your exam! :D

[kristakingmath]

@FireHeop Maybe all calculus teachers need to be nicer!! :)