### Home > CALC > Chapter 12 > Lesson 12.1.1 > Problem12-13

12-13.

Multiple Choice: The arclength of the cardioid given by $x = 2\operatorname{cos} t − \operatorname{cos} 2t$ and $y = 2\operatorname{sin} t − \operatorname{sin} 2t\ (0 ≤ t ≤ 2π)$ can be found by evaluating the integral:

1. $\int _ { 0 } ^ { 2 \pi } \sqrt { 8 - 8 \operatorname { cos } t }\space d t$

1. $\int _ { 0 } ^ { 2 \pi } \sqrt { 8 + 8 \operatorname { cos } t }\space d t$

1. $\int _ { 0 } ^ { 2 \pi } \sqrt { 8 - 8 \operatorname { sin } t }\space d t$

1. $\int _ { 0 } ^ { 2 \pi } \sqrt { 8 + 8 \operatorname { sin } t }\space d t$

1. $\int _ { 0 } ^ { 2 \pi } \sqrt { 5 - 4 \operatorname { cos } t }\space d t$

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