Question

Find the arc length of the polar curve described by: r=9+9cosθ?

Answer 1

Step 1 :

Arc length of a polar curve :

Let f  be a function whose derivative is continuous on an interval .

The length of the graph of is from is .

Step 2 :

The polar curve is .

Since , the curve over is a mirror image of the upper half of the curve over .

So first integrate from and multiply by 2.

Step 3 :

Arc length of the curve the polar curve is .

Let , then .

Thus, arc length of the polar curve is 72.

Solution :

Arc length of the polar curve is 72.