Antiderivative of a distance versus time graph

bobboxx
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What does the antiderivative of a distance versus time graph represent? What does the antiderivative of the anitiderivative of a distance versus time graph represent? I think the units would be meters multiplied by seconds. Thanks.
 
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You are right about the units (assuming metric system). I don't believe there is any physical meaning to this integral.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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