Definite Integration Question 354
Question: $ \int_0^{a}{\frac{xdx}{\sqrt{a^{2}+x^{2}}}}= $
Options:
A) $ a(\sqrt{2}-1) $
B) $ a(1-\sqrt{2}) $
C) $ a(1+\sqrt{2}) $
D) $ 2a\sqrt{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
Put $ t=a^{2}+x^{2}\Rightarrow 2xdx=dt, $ then $ \int_0^{a}{\frac{xdx}{\sqrt{a^{2}+x^{2}}}=\frac{1}{2}\int _{a^{2}}^{2a^{2}}{\frac{1}{\sqrt{t}}dt}} $
$ =[{{(2a^{2})}^{1/2}}-{a^{2/2}}]=a(\sqrt{2}-1) $ .
BETA
