# Lesson Worksheet: Arc Length of a Polar Curve Mathematics

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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Q3:

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

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Q4:

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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Q5:

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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Q6:

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

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Q7:

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

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Q8:

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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Q9:

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

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Q10:

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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