Q. $\int_{}^{}\frac{f^{'}(x)}{\sqrt{f(x)}}\ dx = ... + c;f(x) \neq 0$
A) $\frac{1}{2}\ \sqrt{f(x)}$
B) $2\ \sqrt{f(x)}$
C) $\frac{1}{2}\ f(x)$
D) $2\ f(x)$
Explanation
(b)
Let $I = \int_{}^{}\frac{f^{'}(x)}{\sqrt{f(x)}}\ dx$
Put $f(x) = t \Rightarrow f^{'}(x)dx = dt$
$\therefore I = \int_{}^{}\frac{1}{\sqrt{t}}dt = 2\sqrt{t} + c = 2\sqrt{f(x)} + c\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.