Question

On the interval [0,4] the polar curve r=11(θ^2) has arc length=??? units?

Answer 1

Step 1:

The polar curve is , .

The length of a curve with polar equation , is

Here .

Differentiate with respect to on each side.

Substitute ,   and limits of in length of the polar curve formula. 

Consider .

Differentiate with respect to on each side.

Step 2:

Change of limits:

Lower limit: If , then .

Upper limit: If , then .

Substitute , and change of limits in the integral. 

Solution:

Arc length of the  polar curve is .