# derivative of a definite integral

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• Dec 12th 2012, 08:22 AM
kingsolomonsgrave
derivative of a definite integral
Attachment 26194

is this done by cos(e^3)-cos(e^1)
• Dec 12th 2012, 09:11 AM
emakarov
Re: derivative of a definite integral
$\int_1^3\cos(e^y)\,dy$ is a constant; it does not depend on x. Therefore, its derivative with respect to x is zero.
• Dec 12th 2012, 10:24 AM
hollywood
Re: 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 $\frac{d}{dx}\int_1^x\cos{e^y}dy$? By the Fundamental Theorem of Calculus, it is equal to $\cos{e^x}$.

- Hollywood
• Dec 12th 2012, 03:57 PM
kingsolomonsgrave
Re: 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, 04:00 PM
emakarov
Re: derivative of a definite integral
Quote:

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

Yes.