Question

The expression for arc length in polar form is_________________

(a) \(ds = \int_a^b \sqrt{r^2 + (\frac{dr}{dθ})^2} \)

(b) \(ds = \int_a^b \sqrt{r^2 + (\frac{dr}{dθ})^2} \,dθ \)

(c) \(ds = \int_a^b \sqrt{(\frac{dr}{dθ})^2} \,dθ \)

(d) \(ds = \int_a^b \sqrt{r^2 + (\frac{dr}{dθ})^2} \,dr \)

The question was asked during an online interview.

This interesting question is from Rectification topic in chapter Integral Calculus of Engineering Mathematics

Answer 1

Correct choice is (b) \(ds = \int_a^b \sqrt{r^2 + (\frac{dr}{dθ})^2} \,dθ \)

For explanation I would say: Polar equation is written in terms of polar coordinates r and θ. The right answer is \(ds = \int_a^b \sqrt{r^2 + (\frac{dr}{dθ})^2} \,dθ \).