without evaluating the integral, is the derivative of the function just ?

Thanks in advance for any assistance recieved :)

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- November 10th 2008, 10:30 PMtsal15simple derivative but confusing me
without evaluating the integral, is the derivative of the function just ?

Thanks in advance for any assistance recieved :) - November 10th 2008, 10:37 PMajj86Response
- November 10th 2008, 10:47 PMtsal15
Hey ajj86,

First I gotta say, you've been very helpful within the period of 20mins, more than some others on this forum have been in 20days.

MMM, I believe that you are implying the fundamental theorm of calculus whilst using antidifferentiation techniques aka finding the area under graph aka evaluating the integral...? I'm aware it would be a more perfect answer (can u get more perfect than perfect?), but the question strictly states that i must: "Without evaluating the integral, find F'(x) where F(x) = " so having said that would be the answer?

Thank you

tsal15 - November 10th 2008, 10:52 PMajj86Response
I just found this:

But, I'm not really sure as to whether the answer I gave is correct. Let me do a little more investigating. - November 10th 2008, 11:01 PMtsal15
- November 10th 2008, 11:03 PMajj86Response
According to the form given, I'm thinking the answer would be:

e^(x^2 - 2) - November 10th 2008, 11:06 PMtsal15
- November 11th 2008, 07:05 AMajj86Response
Tsal15, I apologize for not replying last night. I'm not trying to take the easy way out, but I think this might give a better explanation than I can give:

Calculus Facts: Derivative of an Integral

Let me know what you think. - November 11th 2008, 07:25 AMMathstud28
This is just a simple application of the Second Fundamental Theorem of Calculus

The proof of this is most likely beyond the scope of your class. - November 12th 2008, 05:04 AMtsal15
- November 12th 2008, 05:19 AMtsal15
- November 12th 2008, 02:18 PMMathstud28
Wikipedia actually has a pretty non-analysis friendly version. Look here

__Fundamental theorem of calculus - Wikipedia, the free encyclopedia__