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mknut389
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Homework Statement
Consider the path f{r}(t) = (8t, 4t^2, 4log(t) ) defined for t > 0.
Find the length of the curve between the points (8, 4, 0) and (24, 36, 4log(3)).
Homework Equations
[tex]\int[/tex]|r' (t)|dt
The Attempt at a Solution
r(t)=(8t, 4t^2, 4log(t))
r'(t)=(8, 8t, 4/(ln(10)t))
|r' (t)|=[tex]\sqrt{8^2+(8t)^2+(1.737177927/t)^2}[/tex]
|r' (t)|=[tex]\sqrt{64+64t^2+3.01778715219/t^2}[/tex]
At Point (8,4,0) t=1 and at Point (24, 36, 4log(3)) t=3
Therefore the integral is from 1 to 3
from here, the integral of [tex]\int[/tex][tex]\sqrt{64+64t^2+3.01778715219/t^2}[/tex]
is to complex to do by hand, so with MATLAB and TI-89 I am getting an answer of 36.106527, which according to the assignment is wrong. Am I going about this problem wrong? what should I do?
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