Integral Calculus Question 24
Question: $ \int_{{}}^{{}}{\frac{{a^{\sqrt{x}}}}{\sqrt{x}}dx=} $
[Roorkee 1990; MP PET 2001]
Options:
A) $ 2{a^{\sqrt{x}}}{\log_{e}}|a|+c $
B) $ 2{a^{\sqrt{x}}}{\log_{a}}|e|+c $
C) $ 2{a^{\sqrt{x}}}{\log_{10}}|a|+c $
D) $ 2{a^{\sqrt{x}}}{\log_{a}}|10|+c $
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Answer:
Correct Answer: B
Solution:
Put $ \sqrt{x}=t\Rightarrow \frac{1}{2}\frac{1}{\sqrt{x}},dx=dt, $ then $ \int_{{}}^{{}}{\frac{{a^{\sqrt{x}}}}{\sqrt{x}},dx}=2\int_{{}}^{{}}{a^{t}dt}=\frac{2a^{t}}{{\log_{e}}a}+c=2{a^{\sqrt{x}}}{\log_{a}}|e|+c. $
BETA
