An integral in about 7 minutes

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[ezras]

It’s scenic, but also that new camera angle puts you between the camera and whatever you’re writing is & cuts off the rest of the board. The math was great as always, anyways.

[jorex]

That zoom isn’t really necessary in my opinion. It’s not useful and actually quiet distracting.

[UltraMaXAtAXX]

A Laplace transform can be used at the end too, just set s = 1.

[holyshit]

We could also calculate Laplace transform L(sin(t)/t) and evaluate it at s=1

[neilgerace]

I think it's cool that wherever we have e, we can often find π involved as well.

[lordstevenson]

Always love the integral videos, seeing complicated questions broken down to see the many tricks you can use.

[minwithoutintroduction]

رائع كالعادة.
انتظر بشغف جميع أعمالك.

[xizarrg]

The camera cut must have been put in to provide the experience of sitting in the part of the classroom where you can't see the board.

[barsercan]

After 2:45, we can solve it very quickly using Feynman's trick by defining a function of a, which is the integral with sin(ax) instead of sinx. Then we take the derivative and antiderivative in order to find a closed form and use the initial value f(0) = 0 to get f(1) which is the goal integral

[gatocomcirrose]

5:23 but e^ix goes to infinity right? so you have ∞.0

[ytxczwv]

Feynman method would work, let I(b)= integral from o to inf of e^(-bx) sin x /x dx

[Jack_Callcott_AU]

That was great fun Mike. You seem to know some esoteric integral tricks.

[CTJ]

my new headphones make the chalk work very loud

[minecraftkid]

Is the other camera angle new? Nice camera, but maybe it'd be better to out on the right side? Seems like you might block the board less that way.

[motherflerkentannhauser]

Aren't improper integral limits of something? Can you still break things up even if you didn't know individual limits existed or do you still need to follow limit rules?

[Taric]

Wow, that's definitely never something I've seen in Calculus II or Calculus III. I've also taken complex analysis, but I would be hard-pressed to produce that solution on my own.

[MrIStillDontCare]

Any help at 2:17? I can't see why how e^(-x)ln(sin(x) - cos(x)) relates to e^(-x)ln(x)cos(x).

[ericthegreat]

Interesting how taking the integral with respect to y is equivalent to Feinman integration.

[andrewkarsten]

Wait, what about the cos(x) part of the first integral? Handle it the same way?

[tmpqtyutmpqty]

4:08
How does that mean that? The Im is only for the sin