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Vectors : Arc length of a space curve

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Use the integration capabilities of you graphing utility to approximate the arc length of the space curve given by: vector r(t) = t i + t^3 j + 3t K from the point (1,1,3) to the point (2,8,6). Round your answer to the nearest three decimal places.

I did this problem and got the answer 2.003 X 10^10.

Would you please show me how the problem should be done and what the answer should be, even if I am correct?

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Arc length of a space curve is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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if you have a curve r(t) = x(t) i + y(t) j + z(t) k
then the arc length between two points where t=a to t=b is given by

arc length s = int^b_a sqrt( x'(t)^2 + y'(t)^2 + z'(t)^2 ) dt
( this is ...

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