Question

Compute the arc length, in terms of A, a, and b, of the curve r(θ)=A sec(θ) from θ=a to θ=b. You may assume 0 ≤ a ≤ b < π/2 and that A>0?

Answer 1

Step 1 :

The polar curve is , .

Arc length of a polar curve :

The length of the curve with polar equation  , is .

Here .

Consider .

Differentiate with respect to on each side.

Step 2 :

Substitute , and limits of in the arc length formula.

Solution:

Arc length of the curve the polar curve in terms of is .