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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2012-09-28 19:29:25

Hi Anakin;

Good luck at class.

Anakin
2012-09-28 18:08:16

Alright then, I'll go with that as well. Plus it fits the formula from the page you linked. 5 hours until class, I'm gonna catch some sleep.

Thanks Bobbym (and Bob) for the help, I'm very grateful. smile

bobbym
2012-09-28 17:34:03

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.

Anakin
2012-09-28 17:29:37

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.

bobbym
2012-09-28 17:22:28

Hi;

This is what I get plugging into that formula:



Anakin
2012-09-28 17:00:57

Hi Bobbym,

Okay, thanks. I appreciate it!

bobbym
2012-09-28 16:22:58

Hi Anakin;

I am not getting that answer, let me look at it agian.

Anakin
2012-09-28 14:07:20

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?
http://i48.tinypic.com/ej9a9y.jpg

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?

bobbym
2012-09-28 07:33:35

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

Anakin
2012-09-28 07:31:36

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.

bobbym
2012-09-27 18:20:34

Hi;

Do you mean differentiation under the integral sign?

bob bundy
2012-09-27 17:21:27

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

Anakin
2012-09-27 12:56:28

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.

http://i47.tinypic.com/3493ybq.png

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).

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