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Derivative (Integral) = Integral (Derivative)? (Posted on 2012-10-24) Difficulty: 1 of 5
Is d/dx (∫ f(x) dx) equal to ∫ d/dx (f(x)) dx ?

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No Solution Yet Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Solution a math joke + solution./ spoiler | Comment 1 of 3

o    An old math joke.

o    Two male mathematicians (A & B) are in a bar. A  claims that the average person knows very little about basic mathematics. B disagrees, saying that an average   person can cope with a reasonable amount of math.

While A goes off to the restroom, B calls over the waitress. He tells her that in a couple of minutes, after his friend has returned, he will call her over and ask her a question. All she has to do is answer "one third x cubed" and she will be tipped generously. 

 She repeats "one ser -- dex cue"?
He corrects "one third x cubed". 

She: "one thir dex cubed'? 

"-Yes, that's right", he says. So she agrees, and goes off mumbling to herself, "one thir dex cubed", "one thir dex cubed...", … 

 A returns and B proposes a bet to prove his point, that most people do know something about basic math. He will  illustrate  it by asking the blonde waitress to evaluate an integral, and A accepts the 100$ bet.  

 B calls over the waitress (in cahoots with him) and asks "Excuse me, what is the integral of x squared?".

The waitress says "one third x cubed," and while walking away, turns back and says over her shoulder  loud and clear "plus a constant!"   
 

Is d/dx (∫ f(x) dx) equal to ∫ d/dx (f(x)) dx   

    solution:  no! 

  ∫ d/dx (f(x)) dx=d/dx (∫ f(x) dx) +const 

 

Edited on October 24, 2012, 11:05 am
  Posted by Ady TZIDON on 2012-10-24 11:01:54

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