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 June 11th, 2009, 01:18 PM #1 Member   Joined: May 2009 Posts: 58 Thanks: 0 Fundamental Theorem of Calculus Find the derivative of the function : f(x)= ? e^(sint) dt ( limits from cosx to x^2) Answers : f(x)= ? e^(sint) dt ( limits from 0 to x^2)-? e^(sint) dt ( limits from cosx to 0) f'(x) = d/dx ? e^(sint) dt ( limits from 0 to x^2) - d/dx ? e^(sint) dt ( limits from cosx to 0) Let u=x^2 => du=2x.dx; a=cosx => da=-sinx.dx f'(x) = d/du ? e^(sint) dt ( limits from 0 to x^2) du/dx- d/da ? e^(sint) dt ( limits from cosx to 0) da/dx f'(x)= 2x * e^sinu - (-sinx) * e^sina f'(x)= 2x *e^sin(x^2) + sinx * e^sin(cosx) Are these correct? Thank you
 June 14th, 2009, 08:04 AM #2 Senior Member   Joined: Dec 2008 Posts: 251 Thanks: 0 Re: Fundamental Theorem of Calculus Looks good to me; I got the same answer.

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