Solution Found!
Arc length calculations Find the length of
Chapter 11, Problem 17E(choose chapter or problem)
7-18. Arc length calculations Find the length of the following two- and three-dimensional curves.
\(\mathbf{r}(t)=\left\langle\cos ^{3} t, \sin ^{3} t\right\rangle, \text { for } 0 \leq t \leq \pi / 2\)
Questions & Answers
QUESTION:
7-18. Arc length calculations Find the length of the following two- and three-dimensional curves.
\(\mathbf{r}(t)=\left\langle\cos ^{3} t, \sin ^{3} t\right\rangle, \text { for } 0 \leq t \leq \pi / 2\)
ANSWER:Solution 17E In this problem we need to find the length of the curver(t) =The arc length of the curve r(t) from a to b is given by L = ...equation (1) where L denotes arc length.Step 1: Let x= y=Calculate the arc length of the curves for 0 t /2 dr= )+( dt ………….equation (2) =3(-sin t) =3(cos t)dr =+) dt =t +9 )dt =3 sint cost +) dt =3 (sint cos t) dt since [ +=1]