Calculus 2 improper integrals (10 examples)

If Type 1 Improper Integral Converges, Then Type 2 _______?

0:00 5 Round of Improper Integral Battles
0:05 Q1, integral of 1/(2x-1) from 1 to inf vs. from 1/2 to 1
3:55 Q2, integral of 1/(x^2+x-2) fro 2 to inf vs. from 1 to 2
**small mistake, thanks to Pedro for pointing out: at 11:56 should -(1/3)(ln4)**
12:36 Q3, integral of 1/sqrt(x^2-1) from 2 to inf vs. from 1 to 2
19:19 Q4, integral of 1/(x*sqrt(x^3-1) from 2 to inf vs. from 1 to 2
27:40 Q5, integral of tan(x) fro 0 to inf vs. from 0 to pi/2

[bleddyndavies]

I love you bprp, cause of your channel I got a deeper interest in Maths and have signed up for the UKMT mentoring scheme <3

[mooblerthomson]

Thank you so much for making these videos I love calculus and anytime I’m stuck you are always the first place I check for explanations. The way you explain things is so easy to understand and you always show tricks and short cuts that I’ve never been taught in class that are immensely helpful.

[nikolacatic]

Man thank you for sharing your knowledge with us. Thanks to your integrals and derivates I got into Faculty of Technical Sciences. I bow to you!

[zrksyd]

7:00
I actually thought of (x-1)/(x+2) as 1 - (3/(x+2)), which approaches 1 - 0 as you go to infinity. I feel like that's easier to explain that L'opital's rule.

[cosmo]

Reminds me of the old integral battles, so cool!

[omshandilya]

i also want to become a mathematician like you watching this at 2AM

[turtlellamacow]

The third one is easier and cleaner with the change of variable x = cosh(u), but I don't know if hyperbolic functions are part of your curriculum. Of course the answer, arccosh(2), is the same numerically.

[Silvarx]

You can also do: ln(1/4) = ln(1) - ln(4) = 0 - ln(4) = -ln(4)

[stigastondogg]

When you get to the final answers in your videos I feel compelled to applaud

[srnjnmedhi]

Seriously, blackpenredpen is one of my favourite YouTubers.

[nicogehren]

great questions Mr.bprp thanks from Brazil

[rodricrack]

Please, someone. What are the songs names (the 0:00 is the most important to know)? Thanks

[lucasvic]

Nice, Thanks very much. It is very helpful.

[luiseduardoortizortiz]

About the first integral battle, I did it but I got (1/2)*Ln|x-1/2| instead (1/2)*Ln|2x-1|, I derived them and the result was the same in both cases. I wonder if they are two different functions why both of them are integral of the same function?
Greetings from Colombia

[Arpan.Das.]

I'm from India 🇮🇳.
Your video is very helpful for me.

[diffusegd]

Evaluate integral of e^-(x^4) from -infinity to +infinity

[GSHAPIROY]

Another small mistake, at 16:39, you forgot to close the absolute value.

[Daniel-efgg]

(x-1)/(x+2) = (x+2-2-1)/(x+2) = 1 - (3/(x+2)). When x->inf, this just goes to 1.

[josebeleno]

Hi. I have a question in the integral of tan(x) from 0 to infinity. I have learned that if you integrate from [a, b] and there´s a vertical asymptote at c where a<c<b, then you have to split the original integrals in two, s.t you integrate first from [a, c] and then from [c, b]. But tan(x) has many vertical asymptotes, how do you take that into account?

[LuVD]

💯, what have you study?(for example, engineering. I do not know, sorry)