# Worksheet: Arc Length of Parametric Curves

In this worksheet, we will practice using integration to find the arc length of a parametrically defined curve.

**Q5: **

Express the length of the curve with parametric equations and , where , as an integral.

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**Q6: **

Find the length of the curve with parametric equations and , where .

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**Q7: **

Express the length of the curve with parametric equations and , where , as an integral.

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**Q8: **

The position of a particle at time is . Find the distance the particle travels between and .

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**Q9: **

Find the length of the curve with parametric equations and , where .

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**Q10: **

Find the length of the curve with parametric equations and , where .

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**Q11: **

Find the length of the astroid with parametric equations and , where .

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**Q12: **

Find the length of one arch of the cycloid with parametric equations and .

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**Q13: **

Consider the parametric equations and for .

Express the arclength of this curve as an integral.

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Evaluate the integral.

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**Q15: **

Find the arc length of the curve defined by the parametric equations and .

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