Integral Calculus Question 468
Question: $ \int{\frac{{e^{\sqrt{x}}}}{\sqrt{x}}dx}= $
[DCE 1999]
Options:
A) $ {e^{\sqrt{x}}} $
B) $ \frac{{e^{\sqrt{x}}}}{2} $
C) $ 2,{e^{\sqrt{x}}} $
D) $ \sqrt{x},.,{e^{\sqrt{x}}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ I=\int{\frac{{e^{\sqrt{x}}}}{\sqrt{x}}dx.,} $ Put $ \sqrt{x}=t $ ,
$ \therefore \frac{1}{2\sqrt{x}}dx=dt $ \ $ I=2\int{e^{t}dt=2e^{t}+C=2{e^{\sqrt{x}}}+C} $ .
BETA
