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Math Help - definite integration

  1. #1
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    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}?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by vassago View Post
    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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