definite integration

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December 23rd 2008, 10:47 AM
vassago

definite integration

i'm having trouble with this problem because it looks different to me.
on [5,7], $\frac{d}{dt}\sqrt{4+1t^4}dt$
what do i do with the $\frac{d}{dt}$ ?
December 23rd 2008, 10:55 AM
Chris L T521

Quote:

Originally Posted by vassago

i'm having trouble with this problem because it looks different to me.
on [5,7], $\frac{d}{dt}\sqrt{4+1t^4}dt$
what do i do with the $\frac{d}{dt}$ ?

$\int_5^7\left[\frac{\,d}{\,dt}\sqrt{4+t^4}\right]\,dt$

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

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