Fourier Series: The Integrals of Periodic Functions

1. Introduction To Fourier Series
2. Integration of Periodic Function
3. Integration of Functions over a single period
4. Integral of sin nx cos mx
5. Integral of cos mx sin nx
6. integral of sin nx sin mx
7. How To integrate Fourier Series
8. How To solve for Integrals of Periodic Functions
You can learn more by clicking Any of These Links;
Fourier Series & Periodic Function: • Fourier Series & Perio...
EMA382 | Engineering Mathematics IV For Uniben 300 Level Students: • EMA382 | Engineering M...
#fourier
#fourierseries
#periodicfunction
#integration
#integral
#ema382
#engineeringmathematics

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[@AVITECHNOLOGIES]

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[@sadiqyunusa7530]

Kindly solve this Fourier series for me :
Find the Fourier series of the functions below :
F(s) = 1 -pi less than or equal to x less than or equal to 0, X 0 less than or equal to x less than or equal to pi}
When it has a period of 2pi
F(x) = 0 0 less than or equal to x less than or equal to pi, pi less than or equal to x less than or equal to 2pi}
Over a period of 2pi

[@AVITECHNOLOGIES]

Kindly follow the videos on this very playlist, to learn all about Fourier Series.
czcams.com/video/aK-XmuHVzhQ/video.html
You've just started the playlist, proceed and you'll understand how to go about solving your questions.

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[@AVITECHNOLOGIES]

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[@gameliadeti2967]

Meaning in example 4, you were trying to use integration by parts

[@AVITECHNOLOGIES]

No.
That's not integration by parts.
I substituted sin²nx with ½(1-cos2nx). This substitution is from Trigonometric identities.

[@gameliadeti2967]

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Even finding the period of a function such as trig functions, i did not even understand it in class until last night i came across your video that explains it better.God bless you you are really doing good job.
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[@olajumokeoyejide3826]

Please where does the 1/n comes from during the integration .. can’t figure out where it comes from .. you mentioned that you integrate Sin nx = cos nx … where does the 1/n comes from ..? Thanks for your responds

[@AVITECHNOLOGIES]

The integral of sin(nx) is equal to 1/n × cos (nx). When integrating, you need to differentiate the angle, in this case the angle is nx, so, if you differentiate with respect to x, you will get n. So, evaluate 1/ (the derivative) × cosnx.
This is the basic rule of integration of Trigonometric functions. Revisit Trigonometric integration for better understanding. I'll search my videos, and when I find it, I'll send it.
I could not find any of my videos for trigonometric integration. Work with these examples.
1. Integral of sin3x dx= 1/3 × - cos 3x + C
Final answer = (- 1/3)cos3x + C
2. Integral of cos(2x+3) dx = 1/2 × sin(2x+3) + C
Final Answer= (1/2)sin(2x+3) + C
I hope this helps.

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[@AVITECHNOLOGIES]

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[@user-ed3qg7jr5j]

Welldone bruh... May i request how u got -1/n when u solved for the integral of sin nxdx...? I agree the integral of sin x is -cos x but how it became 1/n isnt clear

[@AVITECHNOLOGIES]

When you integrate, you have to differentiate the nx. So, to integrate sinnx DX, first differentiate nx, which is n, then integrate sine, which is - cosine. To write your final answer, write the inverse of your derivative and multiply by the integral of sine.
Integral of sin(nx)DX= 1/n × -cos(nx)+C= -1/n cos(nx).
This is a basic rule in integration.

[@olajumokeoyejide3826]

@@AVITECHNOLOGIESseen the responds here .. thanks

[@AVITECHNOLOGIES]

You are welcome 😊

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[@AVITECHNOLOGIES]

It's your internet connection. CZcams sets video quality according to your data connection. You can change this by clicking the three dots on the screen(top right corner) or settings icon while watching a video, select quality, select advanced and choose 1080p.
Also, Watch the videos with full screen display.

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