Lesson: Arc Length of a Polar Curve

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

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.

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

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