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Re: Fundamental theorem problem


On 7/23/04 at 6:01 AM, jonakst at gw.kirkwood.k12.mo.us (Steven Jonak)
wrote:

>I input the command: D[Integrate[Sec[t],{t,1,x^4}],x] expecting to
>get 4x^3 Sec[x^4] but instead got a fairly complicated result that
>doesn't resemble what one would expect from the Fundamental Theorem
>of Calculus.
>What am I doing wrong? Help!

I don't think you are doing anything wrong. Mathematica 5.0 by default attempts to give all of the conditions needed to make the result of Integrate valid. I suspect this is what you are seeing. This characteristic can be disabled by using GenerateConditions->False. So, if you do

D[Integrate[Sec[t],{t,1,x^4},GenerateConditions->False],x]//Simplify

you will get the result you were expecting.
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