Type 1 improper integrals! calculus 2

We will solve 8 type 1 improper integrals for your calculus 2 class. A type 1 improper integral means we have to integrate over an infinite interval, such as from a to infinity, from negative infinity to b, or from negative infinity to positive infinity. An improper integral is a combination of integral and limit. So you must remember all the integration techniques and also how to take the limit.

0:00 how do we do improper integrals (type 1 improper integral, 8 examples)
0:12 integral of 1/(x+1)^(3/2) from 0 to inf
3:17 integral of x^2/sqrt(x^3+4) from 0 to inf
5:59 integral of e^(1/x)/x^2 from 1 to inf
9:28 integral of ln(x)/x^2 from 1 to inf
13:36 integral of x/(1+x^4) from 0 to inf
17:11 integral of x*e^x from negative inf to 0
21:20 integral of cos(x) from 0 to inf
23:14 integral of 1/(x^2-x) from 2 to inf

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[asianhero.]

I really am blessed to be living in a time like this in terms of math learning. The trick you used for integration by parts was nuts and I would have never known it existed without this video. Great job.

[dhavalsaxena]

I like how maths works a week ago id know what was going on in his videos and once i started my integration classes, a week later i am able to understand every single thing.

[nvapisces]

The last question integral can be done by factoring x² and moving it to the numerator for the integral to become x^(-2)/(1-x^(-1)). Numerator is exactly the derivative of the denominator which gives you the result of the improper integral without solving the partial fractions

[anshumanagrawal]

23:04 The divergence of this Integral is similar to the divergence of the Infinite GP with Common Ratio -1, if you look at the graph of cosine x, it's area till any positive number, starting from 0, ranges between -1 and 1. And, it keeps doing so in a fix pattern, never approaching anything

[haimanotsimegn]

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[nilberthsouza]

Very good. Your videos helped me improve a lot in Calculus. Thank you!

[Miki-dgmd]

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I can gave good information .keep it up.
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[neilgerace]

3:43

::x sees a difficult integral::
::u comes along::
u says, "I'm in my happy place ... I'm in my happy place .. I'm in my happy place..."

[anshumanagrawal]

17:09 Is still find it weird that the area under the graph of a purely algebraic function, has π in it

[fedibaklouti]

the first example id false, you have to Either change u back to x+1, or to make it equals 2 in the left side

[AmanyaOctavias]

thank you very much sir u have enabled me to understand improper integrals

[prudencekamara]

I hate it when he smiles go fo difficult things 😅😂😂😂
Anyway he's a genius ❤️

[DavideCosmaro]

24:25= factoring x^2 would've left you with 1/(x^2 (1- 1/x)) and in if u= 1- 1/x then du= 1/x^2 and the whole integral becomes 1/u

[syz]

The way the infinity is substituted as the limit is not correct. You have to make a definite limit and then take the limit to the infinity. If the limit diverges then you have to use Cauchy's Principal Value theorem. Just wanted to make sure everybody gets the correct way of doing it.

[Taro-wduo]

Im confused, he plugs in the values for u without replacing u back with its x term, doesn’t he have to change the integration bounds? Or does it not matter for infinite stuff

[backyard]

those are easy, on my test we'd get improper integrals that couldn't be integrated. instead we had to use different tests for convergence

[BrillantBABOKA]

Très bonne vidéo, j'ai beaucoup appris de celle ci. Cependant à 18:21, je pense que la réponse est 1-e au lieu de -1+e. Vérifiez svp, car lorsqu'on inverse les bornes d'une intégrale, On multiplie l'intégrale par le signe -, chose qui n'a pas été faite dans ce cas. Depuis le CAMEROUN

[EmpyreanLightASMR]

Diverges to DNE is the name of my black metal doom goth project

[MicklanOfficial]

This video has made me a better person 😭💔🙌🙌🙌

[Emine-riex]

example 4 why don't you substitute 1 and infinity in lnx as the pervious example