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jamonathin

Wed Apr 18, 2007 6:51 pm


Calculus Integral Help

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Hey all, finals are here and i cant figure out how to do this problem:


Let g(x) = x²∫x³  sint²

Evaluate g'(pi) to four deimal places 
where x² is at the bottom right of the ∫ and x³ is at the top right.

My idea of that to do is:

g'(x) = sin(x³)² · (x³)' - sin(x²)² · (x²)'

then sub in:  x = pi

Which is kind of from the "Fundamental Theorom of Calculus" (FTOC) and Chain Rule, but cant find anywhere to verify this.



EDIT: Martin solved it  :)

(1/2)(x³ - cos(x³)sin(x³)) - x² + cos(x²)(sin(x²))


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Brightguy

Wed Apr 18, 2007 9:02 pm


Re: Calculus Integral Help

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Wait, is that the solution for g'(x)?  I get [tex]\textstyle g'(x) = 3x^2\sin(x^6)-2x\sin(x^4)[/tex], which doesn't match.  Yeah, this is a FTC question.


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Cervantes

Wed Apr 18, 2007 10:16 pm


RE:Calculus Integral Help

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I'd have to agree with Brightguy on this one.