Integral of x over tan(x) from 0 to π/2.
Prime Newtons
23,559 views
This integral led me to the classic integral of ln(sinx) which uses the technique popularly known as the King's Rule.
An integral with a classic result
20 Comments
@perpetgholl5742 1 year ago
As you've changed your place, i'm glad to hear the same nice schalke sound.
@gupilsharma3289 1 year ago
The intro looks like I'm about to watch one hell of a great movie.
Love your teaching style and voice sir!
Love your teaching style and voice sir!
@AWittyPerspective 1 year ago
You make people fall in love with the subject. Amazing work!! You are able to teach in such a fun way because you find it fun yourself. Keep going!!
@Gabrielbennett30 1 year ago (edited)
Great problem! I just wanted to point out a small technical detail: the antiderivative of cos(x)/sin(x) should be written as ln|sin(x)| since sin(x) can be negative for some real values of x, and the natural logarithm is only defined for positive arguments in the real number system. Just thought I'd point that out. I know you're plugging in specific values for x, but in general, absolute values are good to incorporate.
@SH1234 1 year ago (edited)
Summary=> ∫(x/tanx).dx
=∫xcotx.dx [0 to π/2] =.
x.lnsinx - ∫lnsinx dx =
(0-0)- (-πln2)/2=(πln2)/2
=∫xcotx.dx [0 to π/2] =.
x.lnsinx - ∫lnsinx dx =
(0-0)- (-πln2)/2=(πln2)/2
@AdrianRif 3 months ago
Very clear and concise explanation. I wish I had math teachers like you at college.
@桜木秋水 1 year ago
This is an amazing channel!
It's very easy to understand and the writing is beautiful!!
It's very easy to understand and the writing is beautiful!!
@HighField-qr6bl 1 year ago
Love it! I could imagine having to invent L'H Rule to get the right answer to things we can visualize like this. Find an infinity and find some new elegance hiding behind it.
@allinmatache1235 1 year ago
if you were my classmate in 11th grade I would have copied your homework no doubt <3
@nickmorris8993 1 year ago
Love the new mega-board. Brilliant and entertaining teaching, as always from the maths guru!
@michaelstahl1515 1 year ago (edited)
I enyoed your video again . I often search for such problems .
Integral of x over tan(x) from 0 to π/2.
Prime Newtons
23,559 views
This integral led me to the classic integral of ln(sinx) which uses the technique popularly known as the King's Rule.
An integral with a classic result