Problem

一、單選題

3. Which of the following integrals gives the length of the graph $y=\sin(\sqrt{x})$ between $x=a$ and $x=b$, where $0<a<b$?

(A) $\int_a^b \sqrt{x+\cos^2(\sqrt{x})}\,\mathrm{d}x$

(B) $\int_a^b \sqrt{1+\cos^2(\sqrt{x})}\,\mathrm{d}x$

(C) $\int_a^b \sqrt{\sin^2(\sqrt{x})+\dfrac{1}{4x}\cos^2(\sqrt{x})}\,\mathrm{d}x$

(D) $\int_a^b \sqrt{1+\dfrac{1}{4x}\cos^2(\sqrt{x})}\,\mathrm{d}x$

(E) $\int_a^b \sqrt{\dfrac{1+\cos^2(\sqrt{x})}{4x}}\,\mathrm{d}x$。