An exponential trigonometric integral.

Рет қаралды 30,123

3 жыл бұрын

We calculate the value of a nice integral involving an exponential trigonometric function.
Playlist: • Interesting Integrals
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Пікірлер: 95

@rbdgr8370 3 жыл бұрын

keep the more saturated colour scheme more often. Adds quality to your production

@demenion3521 3 жыл бұрын

this unsatisfying feeling of having a sum as the result of an integral... ^^

@cphVlwYa 3 жыл бұрын

This is also a beautiful integral to solve with type one contour integration. First realize that due to the symmetry of the cosine function the integral will also be equal to 1/2 the same integral from 0 to 2π.

@goodplacetostop2973 3 жыл бұрын

12:55

@macfrankist 3 жыл бұрын

Im a physicist and love watching the problems you work on.

@nathanisbored 3 жыл бұрын

Thinking about it, I guess for math videos it always makes sense to have color contrast turned way up. In a normal KZfaq video it would look odd and unnatural to do that cuz it messes with skin color and stuff, but in a math video you mainly care about the stuff on the board, and color contrast is just gonna make the colors more vibrant and easy to parse. It seems like it could be strictly better for this kind of presentation. One of the main reasons I like your videos is because of the very vibrant colors on the board, and I feel like upping color contrast would only make that effect stronger.

@soumadipsen8097 3 жыл бұрын

I wonder why, This channel is so good, the topics, the questions, which are not there even in the paid platforms on internet, is available here, still the views and subs are so less....:(((((

@tylershepard4269 3 жыл бұрын

Enter the modified Bessel function. Similar integrals come up when studying class C power amplifiers!

@GaryTugan 3 жыл бұрын

holy crap. and I love the end: "and that's a good place to stop". Mind Blown

@KhaledRadwan-ku2bh 3 жыл бұрын

Another way:

@user-iz6gi1rf4t Жыл бұрын

The series representation of exp-function with trig power leads to series with integrals of (cos(x)^2n) from 0 to pi/2. Using the formula for such integrals we have same answer

@knode1993 3 жыл бұрын

I think this is the Only channel whicj discusse this kind of problem EVERY DAY.

@FunctionalIntegral 3 жыл бұрын

This would have been a good exercise for application of complex analysis!

@ericwilliams6519 3 жыл бұрын

When we're swapping the order of the infinite sum and the integral, wouldn't we need to show the series is uniformly convergent? I'm sure it works out, but that would be another detail in the proof, right?

@bebarshossny5148 3 жыл бұрын

Please do a video at one point on when and why we can switch the order of integration and summation

@covfefe18225 3 жыл бұрын

It's the modified Bessel Function I_0(2). I turned this sum into a hypergeometric function and figured out it was 0F1, so I immediately realized that it was a Bessel function.

@Notthatkindofdr 3 жыл бұрын

Today I taught my calculus class (online) about Riemann sums and showed them I was wearing Michael's "My favorite equation" T-shirt that I got for my birthday this month. :-)

@MohitRaj-1712 3 жыл бұрын

Big fan of your videos. Keep making these videos. These videos help me in developing approach to a Maths 'Problem

@Kierio04 3 жыл бұрын

Lol I’m just watching this and going “why can’t he just integrate it normally”

@EADgbeist 3 жыл бұрын

I'm confused with the second "tool". Is 'm' an integer? I integrated and obtained sin(m*pi)/(m*pi)... which is indeed zero when 'm' is a non-zero integer.