The problem states, r(t)=(6t,3t^2,3log(t)), find the length from the points (6,3,0) and (24,48,3log(4)). I thought it would be the integral from 1-4 of the square root of the derivatives of each squared, added together. Seems that this isn't correct.
My derivatives are r'(t)=(6,6t,3/(tln10))
My final answer is 48.928761 but this was NOT correct. Can someone offer some help here?
This may be confussing: though we're taught in high school, and thus we're used, to
take (as it's usual in conventional hand calculators), in
fact many mathematicians see both log and ln as one and the same.
In fact, when I saw your question that's the first thing I thought, namely: that we have
here log = the natural logarithm (i.e., ln) and not logarithm to base 10.
This was the whole problem...