Integral of tan(x) from 0 to pi/2

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Integral of tan(x) from 0 to pi:2,

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blackpenredpen | 曹老師

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Divergent integrals:
A person: *try to calculate the answer*
bprp: hmm...

Lamiranta

Anyone else know nothing about maths but still watch this guy for his enthusiasm?

tomaszlosinski

I haven't heard him say "Isn't it?" for a long time. I miss that.

rodbhar

Oooooh you sound exhausted ! You should take some rest !

1/(1-x)

nicolasgoubin

The integral of tan x is -ln |cos x|, which by properties of logarithms equals ln |cosx|^-1, which is ln |1/cosx|, which is ln |secx|

Took me a bit to remember to use the properties of logarithms

zachh

4:00 you could say "the angle is like 3.14/2" ))))

legoushque

If you take the new variable t = cos x you get the integral of 1/t from 0 t0 1 which gives the same answer : inf.

renesperb

It does not have a concret area, because it will never reach the asimptote and the area will be infinity. If the integral was from 0 to a number that is smaller than pi/2 even by then it would have a result =).

bbbftpw

Could you do a video on sin(x^2)'s area between 0 and pi? Taylor Polynomial vs. Trapezium Rule

gaminginrealtime

wow, i wouldnt have expected it to diverge. i guess the only way to find out is to do the problem and trust our limits

trace

Integral of floor(tan(x))

(impossible to really calculate but it's equal to gamma(i))

benjaminbrady

Make a video on convergence test of an alternating series.

madhurjyalalung

I always find the divergent exercises slightly depressing at the end...like we did all that work and we didnt even get a number out of it. 😔

XXgamemaster

There's an ad in MAA Focus saying "Potential =" and this very integral.

pierreabbat

When I saw the title of the video I went "What, an easy video, he normally does harder ones" then I tried doing the problem

Lucas-zdhl

O! I want please try solve integral (sinx* sqrt(sinx))

habeebshaalan

Why you are deleted your video about e as infinite sum using binominal theorem?

timka

Somehow that was my first instinct. Well... 😂

gamechep

6÷2(1+2)=?
1st method :- 6÷2(1+2)=6÷2(3)=3×3[according to the Bodmas rule]
=9
2nd method :-
6÷2(1+2)=6÷{2(1+2)}[as x÷2y means x divided by 2y]
=6÷{2(3)}=6÷6=1
Which answer is correct?

bhaskardas

I'm afraid some people will think the surface had to be infinite because of the hole. Video suggestion : something with a similar shape, but with a finite area
-ln(1-x) from 0 to 1 would be cool :)

joluju

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