Attachment 26194

is this done by cos(e^3)-cos(e^1)

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- Dec 12th 2012, 07:22 AMkingsolomonsgravederivative of a definite integral
Attachment 26194

is this done by cos(e^3)-cos(e^1) - Dec 12th 2012, 08:11 AMemakarovRe: derivative of a definite integral
$\displaystyle \int_1^3\cos(e^y)\,dy$ is a constant; it does not depend on x. Therefore, its derivative with respect to x is zero.

- Dec 12th 2012, 09:24 AMhollywoodRe: derivative of a definite integral
The answer emakarov gave is correct, but I'll bet you copied the question incorrectly. Either that or you got a trick question. Did you perhaps mean $\displaystyle \frac{d}{dx}\int_1^x\cos{e^y}dy$? By the Fundamental Theorem of Calculus, it is equal to $\displaystyle \cos{e^x}$.

- Hollywood - Dec 12th 2012, 02:57 PMkingsolomonsgraveRe: derivative of a definite integral
it was a trick question, thanks!

what if it were defined on from 2 to x would we still have cos e^x as the derivative of the integral?

MH - Dec 12th 2012, 03:00 PMemakarovRe: derivative of a definite integral