# Worksheet: Arc Length of Parametric Curve

In this worksheet, we will practice finding the arc length of a parametrically defined curve.

**Q1: **

Calculate the arc length of over the given interval .

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**Q2: **

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

**Q3: **

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

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**Q4: **

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

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**Q5: **

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

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**Q6: **

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

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**Q7: **

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

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**Q8: **

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

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**Q9: **

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

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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 curve with parametric equations and , where .

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**Q12: **

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

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**Q13: **

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

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**Q14: **

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: **

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

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