Question

Find the exact length of the curve. Use a graph to determine the parameter interval.

Answer 1

Step 1:

The equation of the curve is .

Length of a curve with a polar equation , is .

Graph:

Graph the curve .

Graph of the function is drawn for the interval  .

Differentiate with respect to on each side.

Substitute , and limits of in .

Let

.

Answer 2

Continued...

Step 2:

Consider .

Consider .

Let

Differentiate on each side with respect to .

Change of integral  limits:

Upper limit: If

Lower limit: If

Substitute , and limit values in Equation (1).

Substitute values in .

Arc length of the curve is .

Solution:

Arc length of the curve is .