Type 2 improper integrals! calculus 2

We will go over 8 type 2 improper integrals for your calculus 2 class or AP calculus BC class. A type 2 improper integral means we have a vertical asymptote on the interval that we are integrating. Keep in mind, 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 2 improper integral, 8 examples)
0:17 integral of e^(1/x)/x^2 from 0 to 1
3:07 integral of 1/(x*sqrt(ln(x)) from 1 to e
5:40 integral of tan(x) from 0 to pi/2
8:13 integral of (ln(x))^2/x from 0 to 1
10:35 integral of 1/sqrt(1-x^2) from 0 to 1
12:44 integral of 1/cbrt(x) from -1 to 8
17:40 integral of 1/x^4 from -2 to 1
21:57 integral of 1/(x^2+x-2) from 1 to 2

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[benmiddleton]

This guy's the goat i got an exam tomorrow and I feel way more confident thank you so much

[andreki]

very useful video. way better than the real analysis lecture notes from my "top-class" school

[ryancantpvp]

20:43 misteak
-(-1)/[3(-2)^3]
= 1/[3(-8)]
= -1/24
Also
(-1)/[3(1)^3]
= -1/3

[petereziagor]

Please consider adding link to practice problems... I've been studying calculus from YouTube

[beachwave]

love u bro im preparing for my first calc 2 exam. im definitely going to ace this shit. calc 2 is my bitch so far. I fucking love this class. I hope sequences and series dont kill me but I think ill be fine. any tips for preparing for calc 2 final? u got a vid for that

[Arter]

I was wondering about one thing. 20:17 moment reminded me about your words in another video. You said you can't integrate 1/x from (-1) to 1 using odd property of the 1/x function, because "(0-) and 0+ can be different". It's not exactly what you said (you were pointing on graph, where 0- and 0+ were different "lengths"), but I still don't quite understand how you can take them different? Why can't they be the same? If I messed smth, don't be rude pls)

[Elpsycongroo]

AT 8:08 if we use -ln(cosx) as the integral of tanx, can we say it diverges because ln(cos(pi/2)) is ln(0) which is

[matmat]

Isnt the (-1)^(2/3) in 20:25 undefined?

[madebye]

the integral of tangent x is -ln|cos x| + c. Or i'm i worng? great video tho

[rpjtv]

don't we have to take the limit of the integral?

[jagula]

Is this official account or you just reupload his videos?

[nguyenduy]

In example 1: When dx= -x^2 du >> 1/x^2 dx = - du >> You forgot "-1" when subsitution into integral. Then the Integral must be -Infinity right?

[aarona]

How do you tell if a function is approaching from positive or negative without looking at the graph?

[charlesreyes]

Hello I Wanna learn calculus plssss do calculus tutorial for beginners and i will sub to all of ur 3 channel if u do calculus tutorial for beginners

[Ppooh]

hi, what happened to the negative at 3:03 ? shouldnt it be included?

[dpmike]

I thought you need to take the LIMIT of an improper integral?

[Earlxn_Music]

POV: you are a student @UL and chuene gott you here