June 11th, 2009, 02:18 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, 09:04 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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