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:
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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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:
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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