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 Calculus Calculus Math Forum

 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. Tags calculus, fundamental, theorem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post daeng Calculus 1 January 28th, 2014 11:22 PM layd33foxx Calculus 3 December 12th, 2011 07:32 PM riotsandravess Calculus 3 November 25th, 2010 12:44 PM Aurica Calculus 1 June 10th, 2009 05:39 PM mrguitar Calculus 3 December 9th, 2007 01:22 PM

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