Arc length calculations Find the length of the

Chapter 11, Problem 8E

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QUESTION:

7-18. Arc length calculations Find the length of the following two- and three-dimensional curves.

\(\mathbf{r}(t)=\langle 4 \cos 3 t, 4 \sin 3 t\rangle, \text { for } 0 \leq t \leq 2 \pi / 3\)

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QUESTION:

7-18. Arc length calculations Find the length of the following two- and three-dimensional curves.

\(\mathbf{r}(t)=\langle 4 \cos 3 t, 4 \sin 3 t\rangle, \text { for } 0 \leq t \leq 2 \pi / 3\)

ANSWER:

Solution 8E  

We first need the tangent vector and its magnitude

Step 1:

                 

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