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#1 2012-09-27 12:56:28
- Anakin
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Derivative of a definite integral
Hello! I was just working on a review assignment and in the 10% or so left, I've come across a question for which I have no idea on how to begin.
I've looked into the http://en.wikipedia.org/wiki/Leibniz_integral_rule but I'm not sure if that is the method I should be employing, as I've never come across it before. Or it is possible that I have but like I said, this is a review assignment and I haven't been in a math course for over 2 semesters so I may have forgotten it.
Any ideas on how to get started? I tried using substitution to express √(1+t^3) using only x but to no avail as the integral of √(1+t^3) itself looks far too long and complicated to be required for such a straightforward question (using a math engine).
#2 2012-09-27 17:21:27
- bob bundy
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Re: Derivative of a definite integral
hi Anakin,
In other words you can substitute into the integral process any alternative variable.
So I cannot see why you should just 'cancel out' the integration with the differentiation and just sub in the limits.
This worked OK with a simple function, but, I confess, I'm not 100% sure on this. As the day moves ahead, hopefully we'll get a second opinion on this.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2012-09-27 18:20:34
- bobbym
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Re: Derivative of a definite integral
Hi;
Do you mean differentiation under the integral sign?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2012-09-28 07:31:36
- Anakin
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Re: Derivative of a definite integral
Bob: If one was to change the variable in the function, wouldn't the intervals on the integral also change?
Bobbym: I mean differentiating the definite integral, with respect to x. Or at least that's what I think the question appears to be asking for.
#5 2012-09-28 07:33:35
- bobbym
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Re: Derivative of a definite integral
Hi Anakin;
A Leibniz integral is an differentiation under the integral sign and is something else. Otherwise Bob is right just cancel the integral and the derivative.
Please look here:
http://en.wikipedia.org/wiki/Differenti … egral_sign
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2012-09-28 14:07:20
- Anakin
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Re: Derivative of a definite integral
Hi,
By looking at the link that you last posted, I was able to get the following solution. Could you tell me if it seems right?
Also, it would seem that simply cancelling the integral and derivative would lead to a different solution - one that is lacking the 4x and sin(x) in front of the square roots.
Which is the right one then?
#7 2012-09-28 16:22:58
- bobbym
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Re: Derivative of a definite integral
Hi Anakin;
I am not getting that answer, let me look at it agian.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#9 2012-09-28 17:22:28
- bobbym
- Administrator
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Re: Derivative of a definite integral
Hi;
This is what I get plugging into that formula:
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#10 2012-09-28 17:29:37
- Anakin
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Re: Derivative of a definite integral
That's exactly what I've got above as well. I'm not sure whether you're simply checking if my work was free of errors or whether that is the solution to the question. Could you clarify?
Also, I meant plugging the intervals into sqrt(1 + t^3) by canceling the derivative and integral out would yield a different answer from the one I got.
#11 2012-09-28 17:34:03
- bobbym
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Re: Derivative of a definite integral
Whenever I have seen the derivative operator in front of an integral like that they have always meant
differentiate under the integral sign. So, I am going with that.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#13 2012-09-28 19:29:25
- bobbym
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Re: Derivative of a definite integral
Hi Anakin;
Good luck at class.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.