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Magazine Problem 214
For the following exercises, find a definite integral that represents the arc length. $$ r=4 \cos \theta \text { on the interval } 0 \leq \theta \leq \frac{\pi}{2} $$
Problem 215
For the following exercises, find a definite integral that represents the arc length. $$ r=1+\sin \theta \text { on the interval } 0 \leq \theta \leq 2 \pi $$
Problem 216
For the following exercises, find a definite integral that represents the arc length. $$ r=2 \sec \theta \text { on the interval } 0 \leq \theta \leq \frac{\pi}{3} $$
Problem 217
For the following exercises, find a definite integral that represents the arc length. $$ r=e^{\theta} \text { on the interval } 0 \leq \theta \leq 1 $$
Problem 218
For the following exercises, find the length of the curve over the given interval. $$ r=6 \text { on the interval } 0 \leq \theta \leq \frac{\pi}{2} $$
Problem 219
For the following exercises, find the length of the curve over the given interval. $$ r=e^{3 \theta} \text { on the interval } 0 \leq \theta \leq 2 $$
Problem 220
For the following exercises, find the length of the curve over the given interval. $$ r=6 \cos \theta \text { on the interval } 0 \leq \theta \leq \frac{\pi}{2} $$
Problem 221
For the following exercises, find the length of the curve over the given interval. $$ r=8+8 \cos \theta \text { on the interval } 0 \leq \theta \leq \pi $$
Problem 222
For the following exercises, find the length of the curve over the given interval. $$ r=1-\sin \theta \text { on the interval } 0 \leq \theta \leq 2 \pi $$
Problem 223
For the following exercises, use the integration capabilities of a calculator to approximate the length of the curve. $$ [\mathrm{T}] r=3 \theta \text { on the interval } 0 \leq \theta \leq \frac{\pi}{2} $$
