Question

The expression for arc length in rectangular form is_________________

(a) \(ds = \int_a^b xy \sqrt{1 + (\frac{dy}{dx})^2} \)

(b) \(ds = \int_a^b \sqrt{1 – (\frac{dy}{dx})^2} \,dx \)

(c) \(ds = \int_a^b \sqrt{(\frac{dy}{dx})^2} \,dx \)

(d) \(ds = \int_a^b \sqrt{1 – (\frac{dy}{dx})^2} \,dx \)

This question was addressed to me in final exam.

This is a very interesting question from Rectification topic in portion Integral Calculus of Engineering Mathematics

Answer 1

Right option is (d) \(ds = \int_a^b \sqrt{1 – (\frac{dy}{dx})^2} \,dx \)

The best I can explain: Rectangular form is represented by x,y and z co-ordinates. The right answer is \(ds = \int_a^b \sqrt{1 – (\frac{dy}{dx})^2} \,dx. \)