# Worksheet: Arc Length of Parametric Curves

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

Q1:

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

Q2:

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

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Q3:

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

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Q4:

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

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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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Q14:

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

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Q15:

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

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