i'm having trouble with this problem because it looks different to me.

on [5,7], $\displaystyle \frac{d}{dt}\sqrt{4+1t^4}dt$

what do i do with the $\displaystyle \frac{d}{dt}$?

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- Dec 23rd 2008, 10:47 AMvassagodefinite integration
i'm having trouble with this problem because it looks different to me.

on [5,7], $\displaystyle \frac{d}{dt}\sqrt{4+1t^4}dt$

what do i do with the $\displaystyle \frac{d}{dt}$? - Dec 23rd 2008, 10:55 AMChris L T521
$\displaystyle \int_5^7\left[\frac{\,d}{\,dt}\sqrt{4+t^4}\right]\,dt$

This is the same as $\displaystyle \left.\left[\sqrt{1+t^4}\right]\right|_5^7$ because when you take the integral of a derivative, you get the function you were originally differentiating, in this case, $\displaystyle \sqrt{1+t^4}$.