Q. The value of $\int_{1}^{4}e^{\sqrt{x}}\ dx$ is
A) $e^{2}$
B) $2e^{2}$
C) $4e^{2}$
D) $3e^{2}$
Explanation
(b)
Let $I = \int_{1}^{4}{e^{\sqrt{x}}dx}$
Put $x = t^{2} \Rightarrow dx = 2t\ dt$
$\therefore I = \int_{1}^{2}{2e^{t}t\ dt = 2\left\lbrack te^{t} - e^{t} \right\rbrack_{1}^{2}}$
$= 2\left\lbrack (2e^{2} - e \right) - e^{2} + e\rbrack = 2e^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.