Periodic Function: Derivative & Integral

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The discussion centers on whether the derivative and integral of a periodic function are also periodic. It is suggested that the derivative of a periodic function may not be periodic, while the integral could be. Participants are encouraged to provide reasoning for their views, using examples like sin(x) + 1 for clarification. The conversation highlights differing opinions on the periodicity of derivatives and integrals. Ultimately, the relationship between periodic functions and their derivatives and integrals remains a topic of exploration and debate.
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Homework Statement


Is the derivative of a periodic function periodic?
Is the integral of a periocic function periodic?

Homework Equations



a function if periodic if f(x)=f(x+p)

The Attempt at a Solution



I think that the derivative won't be periodic but the integral will. I'm not really sure if I'm right or not though.
 
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If this is an opinion poll, I think the opposite is true. Spell out why you think so and we can compare opinions. Try sin(x)+1.
 

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