Find the arclength of the curve defined by $r(t)=i+9t^2j+t^3k$ for $0 \leq t \leq \sqrt28$.
First I found $r'(t)=\langle 1,18t^2,3t^2\rangle$ and so the magnitude of $r'(t)= \sqrt{1+(18t)^2+(3t^2)^2}$ thus the integral from $0$ to $\sqr...
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First I found $r'(t)=\langle 1,18t^2,3t^2\rangle$ and so the magnitude of $r'(t)= \sqrt{1+(18t)^2+(3t^2)^2}$ thus the integral from $0$ to $\sqr...
The Lemma and a sketch of its proof are given below: My questions are: 1- why the diagram that must be commutative looks specifically like this? My profes...
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Ok, I don't know why, but I've seen this question been asked many times, but none of the answers seem to be helpful, yet the problem is quite ob...