Improper Integrals (KristaKingMath)

Improper Integral 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?!”

[Noble]

yeah, you can't really just plug in infinity... you have to sub in a variable and take the limit. It would be the same for any discontinuity.

[hasantarek]

I love your dedication to start this channel. its been 12 years you have been helping the community to learn math. god bless you. 💌

[kristakingmath]

I would! Technically, you should always do that. Personally though, if you're just trying to figure out the answer, I think you can skip that step and go directly to plugging in infinity for x, because you get to the same result. But on homework or on your test, you should definitely replace with t and then take the limit as t goes to infinity. :)

[sbriscoe]

I love how you take time to explain every single step in your videos, even the simple math... Makes it much easier to follow along! Thx!

[peterbushnell]

Great video, cleared up the method for me. A few people are correct in saying that the notation of limits is missing, but as it is only notation it's not that important in this context at all. Really helpful, thank you!!!

[CharlieTheChap]

This is life saving. I'm feeling more and more confident about Calculus as I watch your videos. Thanks for taking the time.

[daco]

These maths videos really are first class .A really good explanation of the use of infinity in this example .Thanks

[jackal]

Great vid!
I figured out a short cut for integral fractions.
S (1/x^3)
-[(1/(n-1X^n-1)]
Here,
-1/(3-1X^3-1)
-1/2X^2 + C
Done and done

[kristakingmath]

definite integral is defined on a finite range. improper integrals are defined on an infinite range, so there is a difference. if you see infinity or negative infinity, you know it's an improper integral. if you see constant limits of integration, then you're dealing with a definite integral. :)

[FallenSkater]

My professor taught us to substitute a variable (b) for infinite when you're calculating. Then you find the limit of your function as b approaches infinite. It still works out to be zero, but it also explains the calculus part of the problem. Either way, thanks for the video.

[kristakingmath]

Yes, it's the value of the integral, which is the area under the curve 1/(x^5), between x=2 and x=infinity. :)

[AFmountranier]

I am glad that you don't assume that people know what is going on. You explain your work very well. Something that I don't really do. I show the bare minimum when I do my homework and tests. Something I know that I have to change. Also, I am taking a test on this stuff on Wednesday. Fun stuff. I have a dollar riding on an A. More incentive to study harder.

[Taha_]

Thank you,  that was really easy to understand and very nice way in explaining ! 

[MyWolfkid]

awesome, thanks for the video. helped out tons. your really good at explaining what everything means

[kristakingmath]

@Masteroftrancegirl If you approach it that way, you have to apply Chain Rule, and divide by the derivative of the inside function, which is x^5. So you'd get (1/x^5)ln|x^5|. Or you can approach it the way I did. :)

[islespatrick]

At first, I was panicking looking at that example, but you explained it so well.

[NGEternal]

If you do this on a test the professor should give you a 0 for the problem because theoretically this is so wrong. You must use a limit statement to explain the infinite growth or else it is a flawed proof.

[jasontobin]

you are the closest to using the IRAC method of analysis, which is very very good. remember: spill the beans up front. Issue. Rule. Application. Conclusion. good stuff all in all. i like how you present the rules and use textbook examples.

[kristakingmath]

@Masteroftrancegirl Thank you! I'm so glad you like it!! :D

[alisawi]

Thank you so much! I love the way you work the problems :)