Question

The arc length of y = cosh⁡x where x varies from 0 to 1 is ____________

(a) \(\frac{e}{2} – \frac{1}{2e} \)

(b) \(\frac{e}{2} – \frac{1}{2e} + \frac{1}{2e} \)

(c) \(\frac{e}{2} – \frac{1}{2e} \)

(d) 2e

I have been asked this question in semester exam.

Question is from Rectification topic in division Integral Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) \(\frac{e}{2} – \frac{1}{2e} \)

Explanation: y’ = sinh⁡x

Arc length = \(\int_a^b \sqrt{1 + (\frac{dy}{dx})^2} \,dx\)

= \(\int_0^1 \sqrt{1 + (sinh⁡x)^2)} \,dx\)

= \(\int_0^1 cosh⁡x \,dx \)

= \(\Big[sinh ⁡x\Big]_0^1\)

= \(\frac{e}{2} – \frac{1}{2e} \).