Definite Integration Question 105
Question: The value of $ \int_0^{2}{\frac{{3^{\sqrt{x}}}}{\sqrt{x}}}dx $ is
[SCRA 1992]
Options:
A) $ \frac{2}{\log 3}.({3^{\sqrt{2}}}-1) $
B) 0
C) $ 2.\frac{\sqrt{2}}{\log 3} $
D) $ \frac{{3^{\sqrt{2}}}}{\sqrt{2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ \sqrt{x}=t $ or $ \frac{1}{\sqrt{x}}dx=2 $ dt Also, as $ x=0 $ to 2 so, $ t=0 $ to $ \sqrt{2} $
Therefore, $ \int_0^{2}{\frac{{3^{\sqrt{x}}}}{\sqrt{x}}}dx=2\int_0^{\sqrt{2}}{3^{t}}dt=2[ \frac{3^{t}}{\log 3} ]_0^{\sqrt{2}} $
$ =\frac{2}{\log 3}({3^{\sqrt{2}}}-1) $ .
BETA
