Integral of cos(x) from 0 to infinity

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In this problem I work out the integral of cos(x) from 0 to infinity. This is a problem from a very old book called Integral Calculus. It was written by H.B. Phillips and it was published in 1917.

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As a student of interval arithmetic, I would accept an interval as an answer.

winklethrall

Very straightforward explanation and wasn't immediately apparent to me before. Thank you.

Jason-bgjc

Cool.. always interesting to watch anything you post, so please dont hesitate to make a video about any kind of or level of math that comes to you. Thnx for the vid!

AceOfHearts

This was super helpful, thank you! I blanked out on what happens if the trig functions has a limit of infinity.

chrissysevigny

If you replace cosx by cos(x^2) this actually converges to a nice value!

anthonyymm

I thought diverges means increasing without bound. In this case I would say the limit is not defined. Is this not correct?

rah

what books do you recommend for learning math from start to finish all the way from the basics to advanced? love ur videos 👍🏻

xaelk

Hello! Again... Dear Math Sorcerer is it true that Numerical Methods can help us to understand better the Calculus? Btw I started to read Numerical Methods Chapra. As always thank you for each video they are like a little push to me in Math's world.

ganimedescabreralanuza

hmmm even though the limit of the integral doesn't exist, we can imagine that since cos(x) goes on forever, every area segment above the x axis is cancelled by its negative mirror image below the x axis

is it *not* possible to say that the integral is zero? where did i go wrong here?

GeoffryGifari

You are a very good teacher. May I ask what you do for a living other than just making math videos for YouTube? Don't answer if you don't want to, I'll respect your decision, but to me you seem like someone with a PhD in math who does research. Btw you are really cool.

soumyadipbanerjee

so the laplace transform of cos(w0*z) does not exist, because the absolute integral of the function does not converge.
but, the fourier transform exits! because of the Euler expression. The complex exponents of the euler transformation directly translate onto the frequency domain.
Mr. Math Wizard, I'd like to ask you this... Why is this so?
Is it because Fourier Transform and Laplace Transform are loosely defined? Some inherent definition problem at the core? Or is it because of the Euler Expression?
Please let me know. Thank you!

ohayuhanna

Studying engineering and we don’t bother with silly limits we just plug in infinity and call it a day 😂 the math sorcerer would keel over if he saw my notation

Spencer_Sp

Is that the same for Lebesgue Integrals?

kanewilliams

question this is just me being an observer and i am by no means a mathematician just curious. What happens to the area of cos(ax) as a approaches infinity but x is bound from -1 to 1. is it just an area of a square. Cant seem to setup the problem when thinking about it. My understanding of cos my be flawed but thinkking was if a approaches ifinity the frequencey approaches what? in my head i see peek to peek gets infinitely close. Do the peeks ever touch? is there such an area where there is no curve but every point on graph touch each other. I know seems impossible since its not a function but cos(ax) is and when a approaches infinity it seems may never touch but the area under the curve feels like it just approaches the area of a square when its bounded.

salsspar

Can we put this under rug by dirac's delta function? Or something?

رضاشریعت

shouldnt we explain why the limit dne ?

ShaolinMonkster

Why in my E&M class does the integral equal zero?

josephanthonycohenbrownsto

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