Your integral is incorrect. It is not \(\int_2^{7.5}3^{-x}dx\) It should be \(\int_2^{7.5}(\frac{1}{2})^{x/3}dx\)
Also, since you previously used x for distance, it would have been clearer to use t in this integral.
(You and I obviously have a different concept of "messy"!!)
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