# Worksheet: Arc Length of a Polar Curve

In this worksheet, we will practice finding the length of a curve defined by polar equations using integration.

**Q1: **

Write the integral for the arc length of the spiral between
and . Do **not** evaluate the integral.

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**Q2: **

The purpose of this question is to get improved estimates on the length of a spiral curve.

Use the fact that when to find lower and upper bounds for the length of the spiral between and . Give your answer to 4 decimal places.

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By comparing to the average of and when , find better bounds for estimating . Give your answer to 4 decimal places.

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**Q5: **

Find the arc length of the polar curve , where lies in the interval .

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**Q6: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

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**Q7: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

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**Q8: **

Find the arc length of the polar curve , where lies in the interval .

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**Q12: **

Find the arc length of the polar curve , where lies in the interval .

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**Q13: **

Consider the polar curve , where lies in the interval . Find a definite integral that represents the arc length of this curve.

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**Q14: **

Find the arc length of the polar curve , where lies in the interval .

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**Q16: **

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**Q22: **

Find the arc length of the polar curve , where lies in the interval .

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**Q23: **

Find the arc length of the polar curve , where lies in the interval .

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**Q25: **

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