Never stop learning. Those who stopped learning have stopped living.

"the beauitful thing is that you generated an answer incorrect" lmao

This guy has impeccable blackboard etiquette. So neat and easy to read.

yikes. can't believe i forgot that lol. incredible how the result is transformed from 4 to 0 from such a simple error

4;23 that is the most beautiful sine graph ive ever seen

Can do in your head if you spot the trick: 2 int[0 to pi] sin(x) dx = 2[cos(0) - cos(pi)] = 4

I'm retired.  I did engineering and meteorology for my entire career.  I never enjoyed calculus in school, it was just a tool to do my job.  It is now fun to watch Prime Newtons just to keep my mind working.

The precision he draws sine curves scares me.

I keep seeing these when I go to listen to ASMR to go to sleep, ITS TOO INTERESTING EVERY NIGHT BEFORE BED I WATCH ONE OF THE VIDEOS......

I loved the comment about pulling the negative sign out of the first evaluation step "just to make things cool"  😂

I have a lot of math under my belt ... No one ever taught that!  Thank you for that insight.

8:53 I respect

"The race is not to the swift" is an appropriate epigram for this problem.

The square root of x^2 is well defined for all values of x, but it has a subtle behavior when x is negative. If, for example, x = -3, then sqrt((-3)^2) = sqrt(9) = 3, so sqrt(x^2) is NOT equal to x if x = -3. Instead, if x = -a is negative (where a is positive), then sqrt(x^2) = sqrt((-a)^2) = sqrt(a^2) = a = -x = |x|. Thus, sqrt(x^2) = |x| is valid if x is any real number, positive or negative or 0.

A good reminder of sqrt() function. In this context, it is the principal value of the square root i.e. the non-negative square root.

Muchas gracias por compartir tan interesante ejercicios de integrales definidas.😊. Mi hija y mi persona estamos muy agradecidos por la buena y clara explicación. 😊❤😊.

Challenged by the thumbnail title: I came up with the answer 4 after roughly 45 seconds of integrating in my head. Seemed so easy, hope I got it right. 😂

This man's chalk game is on point.

im actually flabbergasted from the fact that many cannot comprehend the function co domain shits and just often end up getting these wrong

This is actually a great channel, love the way you explained everything, I haven't learnt integration much and yet I was still able to interpret it very well