Integral Applications: Rate of Change

olicoh
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Hey guys,
I was wondering if you could just check this problem for me (I put it in a Word Document and attached it to this post).

The problem, my work, and my attempted solution is included in it.

Thanks!
 

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looks correct.
 
Very nicely formatted!

A couple of suggestions:
1) Include dt in your integral, like so
\int_0^{15}\left(\frac{40}{(2t + 1)^2}-60\right)dt
2) Write your answer as a sentence, not an equation, and include units.
 
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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