Worksheet: Finding the Length of a Polar Curve

This worksheet assesses your understanding of arc length with polar coordinates and how to use the polar arc length formula (for a parametric curve) to find lengths of polar curves.

Q1:

Find the arc length of the cardioid with polar equation .

Q2:

Find the arc length of the cardioid with polar equation .

Q3:

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

Q4:

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.

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