# 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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Q3:

Let be the arc length of the polar curve over the interval . Express as a definite integral.

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Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

Q4:

Find the total arc length of .

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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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Q9:

Find a definite integral that represents the arc length of on the interval .

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Q10:

Find the arc length of the polar curve given by on the interval .

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Q11:

Find the arc length of the polar curve over the interval .

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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Q15:

Find the arc length of the cardioid .

Q16:

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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Q17:

Find the arc length of the polar curve over the interval .

Q18:

Let be the arc length of the polar curve over the interval . Express as a definite integral.

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Using a calculator, or otherwise, find the value of giving your answer to 3 decimal places.

Q19:

Let be the arc length of the polar curve over the interval . Express as a definite integral.

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Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

Q20:

Let be the arc length of the polar curve over the interval . Express as a definite integral.

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Using a calculator, or otherwise, find the value of giving your answer to 4 decimal places.

Q21:

Find a definite integral that represents the arc length of in the interval .

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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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Q24:

Find a definite integral that represents the arc length of on the interval .

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Q25:

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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