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June 11th, 2009, 02:18 PM   #1
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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
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June 14th, 2009, 09:04 AM   #2
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Re: Fundamental Theorem of Calculus

Looks good to me; I got the same answer.
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