A) \[\frac{1}{3}[{{x}^{3/2}}-{{(x-2)}^{3/2}}]+c\]
B) \[\frac{2}{3}[{{x}^{3/2}}-{{(x-2)}^{3/2}}]+c\]
C) \[\frac{1}{3}[{{(x-2)}^{3/2}}-{{x}^{3/2}}]+c\]
D) \[\frac{2}{3}[{{(x-2)}^{3/2}}-{{x}^{3/2}}]+c\]
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\frac{dx}{\sqrt{x}+\sqrt{x-2}}=\frac{1}{2}\int_{{}}^{{}}{\frac{x-(x-2)}{\sqrt{x}+\sqrt{x-2}}\,dx}}\] \[=\frac{1}{2}\int_{{}}^{{}}{(\sqrt{x}-\sqrt{x-2})\,dx}=\frac{1}{2}\left[ \frac{{{x}^{3/2}}}{3/2}-\frac{{{(x-2)}^{3/2}}}{3/2} \right]+c\] \[=\frac{1}{3}\left\{ {{x}^{3/2}}-{{(x-2)}^{3/2}} \right\}+c.\]
You need to login to perform this action.
You will be redirected in
3 sec
